Table of Contents
See also:  Dates of creation of all indexed pages

Measurements and Units

1. All metric prefixes: Current SI prefixes, obsolete prefixes, bogus prefixes...
2. Prefixes for units of information  (multiples of the bit only)  & brontobyte hoax.
3. Density one. Relative and absolute density precisely defined.
4. Acids yielding a mole of H⁺ per liter are normal (1N) solutions.
5. Calories: Thermochemical calorie, gram-calorie (g-cal), IST calorie (and Btu).
6. Horsepowers: hp, electric horsepower, metric horsepower, boiler horsepower.
7. The standard acceleration of gravity (1G) has been 9.80665 m/s² since 1901. 
   Time:
8. Tiny durations; zeptosecond (zs, 10^-21s) & yoctosecond (ys, 10^-24s).
9. A jiffy is either a light-cm or 10 ms (tempons and chronons are shorter).
10. The length of a second. Solar time, ephemeris time, atomic time.
11. The length of a day. Solar day, atomic day, sidereal or Galilean day.
12. Scientific year = 31557600 SI seconds  (» Julian year of  365.25 solar days).
    Length:
13. The International inch (1959) is 999998/1000000 of a US Survey inch.
14. The typographer's point  is  exactly  0.013837" = 0.3514598 mm.
15. Leagues: Land league, nautical league.
16. Radius of the Earth and circumference at the Equator.
    • Distance between two points at the surface of the Earth.
    • The figure of the Earth. Geodetic and geocentric latitudes.
17. Extreme units of length. The very large and the very small. 
    Surface Area:
18. Acres, furlongs, chains and square inches... 
    Volume, Capacity:
19. Capitalization of units. You only have a choice for the liter (or litre ).
20. Drops or minims: Winchester, Imperial or metric. Teaspoons and ounces.
21. Fluid ounces: American ounces (fl oz) are about 4% larger than British ones.
22. Gallons galore: Winchester (US) vs. Imperial gallon (UK), dry gallon, etc.
23. US bushel and Winchester units of capacity (dry = bushel, fluid = gallon).
24. Kegs and barrels: A keg of beer is half a barrel, but not just any "barrel". 
    Mass, "Weight":
25. Tiny units of mass. A hydrogen atom is about 1.66 yg.
26. Technical units of mass. The slug and the hyl.
27. Customary units of mass  which survive in the electronic age.
28. The  poids de marc  system:   18827.15 French grains  to the kilogram.
29. A talent was the mass of a cubic foot of water.
30. Tons: short ton, long ton (displacement ton), metric ton (tonne), assay ton, etc.
    • Other tons: Energy (kiloton, toe, tce), cooling power, thrust, speed...

    The Art of Rounding Numbers:

31. Scientific notation:  Nonzero numbers given as multiples of  powers of ten.
32. So many "significant" digits  imply a result of limited precision.
33. Standard deviation  gives the  precision  of a result as a form of  uncertainty.
34. Engineering notation  reduces a number to a multiple of a power of 1000.
35. The quadratic formula  is numerically inadequate in common cases.
36. Devising robust formulas  which feature a stable floating-point precision.

    Scales and Ratings: Measuring without Units

37. The Beaufort scale  is now defined in terms of wind speed.
38. The Saffir / Simpson scale  for hurricanes.
39. The Fujita scale  for tornadoes.
40. Decibels:  A general-purpose logarithmic scale for relative power ratios.
41. Sound intensity level (SIL)  is well-defined;  SPL is an  approximation.
42. Apparent and absolute magnitudes  of stars.
43. The Richter scale  for earthquakes and other sudden energy releases.

    Scaling and Scale Invariance

44. The scale of animals  according to Galileo Galilei.
45. Jumping fleas...  compared to jumping athletes...
46. Drag coefficient  of a sphere as a function of the Reynolds number  R.

    Numerical Constants: Mathematical & Physical Constants

    Physical Constants:
47. For the utmost in precision,  physical constants are derived in a certain order.
48. Primary conversion factors  between customary systems of units.
    6+1 Basic Dimensionful Physical Constants  (Proleptic SI)
49. Speed of Light in a Vacuum (Einstein's Constant):   c = 299792458 m/s.
50. Magnetic Permeability of the Vacuum: An exact value defining the ampere.
51. Planck's constant:  The ratio of a photon's energy to its frequency.
52. Boltzmann's constant:  Relating temperature to energy.
53. Avogadro's number:  The number of things per mole of stuff.
54. Mechanical Equivalent of Light (683 lm/W at 540 THz) defines the candela.
55. Newton's constant of gravitation  and a futuristic definition of the second.
    Fundamental Mathematical Constants: 
56. 0:  Zero is the most fundamental and most misunderstood of all numbers.
57. 1 and -1:  The unit numbers.
58. p ("Pi"): The ratio of the circumference of a circle to its diameter.
59. Ö2: The diagonal of a square of unit side.  Pythagoras' Constant.
60. f: The diagonal of a regular pentagon of unit side.  The Golden Number.
61. Euler's  e:  The base of the exponential function which equals its own derivative.
62. ln(2):  The alternating sum of the reciprocals of the integers.
63. Euler-Mascheroni Constant  g :  Limit of   [1 + 1/2 + 1/3 +...+ 1/n] - ln(n).
64. Catalan's Constant  G :  The alternating sum of the reciprocal odd squares.
65. Apéry's Constant  z(3) :  The sum of the reciprocals of the perfect cubes.
66. Imaginary  i:  If "+1" is a step forward, "+ i" is a step sideways to the left.
    Exotic Mathematical Constants: 
67. Delian constant:  2^1/3  is the solution to the classical  duplication of the cube.
68. Gauss's constant:  The reciprocal of the arithmetic-geometric mean of 1 and Ö2.
69. Mertens constant:  The limit of   [1/2 + 1/3 + 1/5 +...+ 1/p] - ln(ln p)
70. Artins's constant  is the proportion of long primes in decimal or binary.
71. Ramanujan-Soldner constant (m):  Positive root of the logarithmic integral.
72. The Omega constant:  W(1) is the solution of the equation   x exp(x) = 1.
73. Feigenbaum constant (d) and the related reduction parameter (a).
    Some Third-Tier Mathematical Constants: 
74. Brun's Constant:  A standard uncertainty  (s)  means a 99% level of  ±3s
75. Prévost's Constant:  The sum of the reciprocals of the Fibonacci numbers.
76. Grossman's Constant:  One recurrence converges for only one initial point.
77. Ramanujan's Number:   exp(p Ö163)   is almost an integer.
78. Viswanath's constant:  Mean growth in random additions and subtractions.

    Counting, Combinatorics, Probability

79. Always change your first guess if you're always told another choice is bad.
80. The Three Prisoner Problem predated Monty Hall and Marilyn by decades.
81. Seating N children at a round table in (N-1)! different ways.
82. How many Bachet squares?  A 1624 puzzle using the 16 court cards.
83. Choice Numbers: C(n,p) is the number of ways to choose p items among n.
84. C(n+2,3) three-scoop sundaes. Several ways to count them (n flavors).
85. C(n+p-1,p) choices of p items among n different types, allowing duplicates.
86. How many new intersections of straight lines defined by n random points.
87. Face cards. The probability of getting a pair of face cards is less than 5%.
88. Homework Central: Aces in 4 piles, bad ICs, airline overbooking.
89. Binomial distribution. Defective units in a sample of 200.
90. Siblings with the same birthday. What are the odds in a family of 5?
91. Covariance:  A generic example helps illustrate the concept.
92. Variance of a binomial distribution, derived from general principles.
93. Standard deviation. Two standard formulas to estimate it.
94. The Markov inequality  is used to prove the  Bienaymé-Chebyshev inequality.
95. The Bienaymé-Chebyshev inequality  is valid for  any  probability distribution.
96. Inclusion-Exclusion: One approach to the probability of a union of 3 events.
97. The "odds in favor" of poker hands: A popular way to express probabilities.
98. Probabilities of a straight flush in 7-card stud. Generalizing to "q-card stud".
99. Probabilities of a straight flush among 26 cards  (or any other number).
100. The exact probabilities in 5-card, 6-card, 7-card, 8-card and 9-card stud.
101. Rearrangements of  CONSTANTINOPLE  so no two vowels are adjacent...
102. Four-letter words from  POSSESSES:  Counting with generating functions.
103. How many positive integers below 1000000  have their digits add up to 19?
104. Polynacci Numbers:  Flipping a coin n times without  p  tails in a row.
105. 252 decreasing sequences of 5 digits  (2002 nonincreasing ones).
106. How many ways are there to make change for a dollar?  Closed formulas.
107. Partitioniong an amount into the parts minted in a certain currency.
108. The number of rectangles in an N by N chessboard-type grid.
109. The number of squares in an N by N grid:  0, 1, 5, 14, 30, 55, 91, 140, 204...
110. Screaming Circles:  How many tries until there's no eye contact?
111. Average distance between two random points on a segment, a disk, a cube...
112. Average distance between two points on the surface of a sphere.

     Stochastic Processes & Stochastic Models

113. Poisson Processes: Random arrivals happening at a constant rate (in Bq).
114. Simulating a poisson process is easy with a uniform random number generator.
115. Markov Processes: When only the present influences the future...
116. The Erlang B Formula assumes callers don't try again after a busy signal.
117. Markov-Modulated Poisson Processes may look like Poisson processes.

     "Utility" and Decision Analysis

118. The Utility Function: A dollar earned is usually worth less than a dollar lost.
119. Saint Petersburg Paradox: What would you pay to play the Petersburg game?

     Mathematical Proofs

120. You can only prove aples).
121. Stochastic proofs  leave only a  vanishing  uncertainty.
122. Heuristic arguments  establish the likelihood of a conjecture.
123. Too few tools  are not enough to prove a given statement.

     Geometry and Topology   (for Polyhedra page, see below)

124. Center of an arc determined with straightedge and compass.
125. Surface areas: Circle, trapezoid, triangle, sphere, frustum, cylinder, cone...
126. Special points in a triangle. Euler's line and Euler's circle.
127. Elliptic arc: Length of the arc of an ellipse between two points.
128. Perimeter of an ellipse. Exact formulas and simple ones.
     • Circumference of an ellipse: Unabridged discussion.
129. Surface area of a spheroid  (oblate or prolate ellipsoid of revolution).
     • Surface area of a general ellipsoid.
130. Surface of an ellipse.
131. Quadratic equations in the plane describe ellipses, parabolas, or hyperbolas.
132. Volume of an ellipsoid [spheroid].
133. Centroid of a circular segment. Find it with Guldin's (Pappus) theorem.
134. Focal point of a parabola. y = x ² / 4f (where f is the focal distance).
135. Parabolic telescope: The path from infinity to focus is constant.
136. Make a cube go through a hole in a smaller cube.
137. Octagon: The relation between side and diameter.
138. Constructible regular polygons  and constructible angles (Gauss).
139. Areas of regular polygons of unit side: General formula & special cases.
140. For a regular polygon of given perimeter, the more sides the larger the area.
141. Curves of constant width: Reuleaux Triangle and generalizations.
142. Irregular curves of constant width. With or without any circular arcs.
143. Solids of constant width. The three-dimensional case.
144. Constant width in higher dimensions.
145. Fourth dimension. Difficult to visualize, but easy to consider.
146. Volume of a hypersphere and hyper-surface area, in any number of dimensions.
147. Hexahedra. The cube is not the only polyhedron with 6 faces.
     • Unabridged discussion.
148. Descartes-Euler Formula: F-E+V=2 but restrictions apply.

     Topology:

149. Metric spaces:  The motivation behind more general  topological  spaces.
150. Topological spaces:  Singling out abstract "open" subsets defines a  topology.
151. Closed sets  are sets (of a topological space) whose complements are open.
152. Subspace F of E:  Its open sets are the intersections with F of open sets of E.
153. Separation axioms:  Flavors of topological spaces, according to  Trennung.
154. Compactness of a topological space:  Every open cover has a  finite  subcover.
155. Complete metric space:  All Cauchy sequences are convergent.
156. Local compactness:  Every point of the set has a  compact neighborhood  in it.
157. General properties of sequences  are indicative of topological characteristics.
158. Continuous functions  are such that the  inverse image  of any open set is open.
159. The product topology  makes projections continuous on a cartesian product.
     • Tychonoff's Theorem:  Any product of compact spaces is compact.
160. Connected sets  cannot be split by open sets; they need not be path-connected.
161. Homeomorphic sets  are related by a bicontinuous function  (homeomorphism).
162. Homotopy:  A progessive transformation of a  function  into another.
163. The Fundamental Group:  The homotopy classes of all loops through a point.
164. Homology and Cohomology.  Poincaré duality.
165. Descartes-Euler Formula:  F-E+V = 2, but restrictions apply.
166. Euler Characteristic:   c   (chi)  extended beyond its traditional definition...
167. Winding number  about point O of a continuous planar curve not containing O.
     • The  dog on a leash theorem.
     • A topological  proof of the fundamental theorem of algebra.
168. Fixed-point theorems  by  Brouwer,  Shauder  and  Tychonoff.
169. Turning number  of a planar curve with a well-defined oriented tangent.
170. Real projective plane  and Boy's surface.
171. Hadwiger's  additive continuous functions of d-dimensional rigid bodies.
172. Eversion of the sphere.  An homotopy  can  turn a sphere inside out.
173. Classification of surfaces:  "Zero Irrelevancy Proof" (ZIP) by J.H. Conway.
174. Braid groups:  strands, braids and pure braids.

     Angles and Solid Angles:

175. Planar angles  separate two directions.  In an oriented plane, they are  signed.
176. Solid angles  are to spherical patches what planar angles are to circular arcs.
177. Circular measures:  Angles and solid angles aren't quite dimensionless quantities.
178. Formulas for solid angles  subtended by patches with simple shapes.

     Curvature and Torsion:

179. Curvature of a planar curve:  The variation of inclination with distance  dj/ds.
180. Curvature and torsion  of a three-dimensional curve.
181. Geodesic and nornal curvatures and torsions  of a curve drawn on a surface.
182. Lines of curvature and geodesic lines.  Lines of extremal curvature or least length.
183. Meusnier's theorem:  Tangent lines have the same  normal curvature.
184. Gaussian curvature of a surface and its integral:  The  Gauss-Bonnet theorem.
185. Parallel-transport of a vector around a closed curve.  Holonomic angle of a loop.
186. Total curvature of a curve.  The Fary-Milnor theorem for knotted curves.
187. Linearly independent components  of the  Riemann curvature tensor.

     Planar Curves:

188. Cartesian equation of a straight line:  passing through two given points.
189. Confocal Conics:  Ellipses and hyperbolae sharing the same pair of  foci.
190. Spiral of Archimedes:  Paper on a roll, or groove on a vinyl record.
191. Hyperbolic spiral:  The inverse of the  Archimedean spiral.
192. Catenary:  The shape of a thin chain under its own weight.
193. Witch of Agnesi.  How the versiera (Agnesi's cubic) got a weird name.
194. Folium of Descartes.
195. Lemniscate of Bernoulli:  The shape of the infinity symbol is a quartic curve.
196. Along a Cassini oval, the product of the distances to the two foci is constant.
197. Limaçons of Pascal:  The cardioid  (unit epicycloid) is a special case.
198. On a Cartesian oval, the weighted average distance to two poles is constant.
199. Parallel curves  share the same normal, along which their distance is constant.
200. The nephroid  (or  two-cusped epicycloid )  is a  catacaustic  of a circle.
201. Freeth's nephroid:  A special  strophoid  of a circle.
202. Bézier curves  are algebraic splines.  The cubic type is the most popular.
203. Piecewise circular curves:  The traditional way to specify curved forms.
204. Intrinsic equation  [curvature as a function of arc length]  may include  spikes.
205. The quadratrix (or trisectrix) of Hippias can square the circle and trisect angles.
206. The parabola  is a curve that's  constructible  with straightedge and compass.
207. Mohr-Mascheroni constructions  use the compass alone  (no straightedge).

     Gears:

208. Glossary  of terms related to gears.
209. Planar curves  rolling without slipping while rotating about two fixed points.
210. Congruent ellipses  roll against each other while revolving around their foci.
211. Elliptical gears:  A family of gears which include ellipses and sine curves.
212. Cycloidal gears :  Traditional profiles used by watchmakers.
213. Epicycloidal gears :  Philippe de la Hire (1640-1718).
214. Involute tooth profile  provides a constant rotational speed ratio.
215. Harmonic Drive:  The  flexspline  has 2 fewer teeth than the  circular spline.

     Polyhedra (3D), Polychora (4D), Polytopes (nD)

216. Hexahedra.  The cube is not the only polyhedron with 6 faces.
217. Fat tetragonal antiwedge:  Chiral hexahedron of unit volume and  least area.
218. Enumeration of polyhedra: Tally of convex polyhedra with n faces and k edges.
     • Counting Polyhedra (1): Table, comments, references...
     • Counting Polyhedra (2): Larger table!
219. The 5 Platonic solids: Cartesian coordinates of the vertices.
220. The 13 Archimedean solids  and their  duals  (Catalan solids).
221. Some special polyhedra may have a traditional (mnemonic) name.
222. Polyhedra in certain families are named after one of their prominent polygons.
223. Deltahedra have equilateral triangular faces. Only 8 deltahedra are convex.
224. Johnson Polyhedra and the associated nomenclature.
225. Polytopes are the n-dimensional counterparts of 3-D polyhedra.
226. A simplex of touching unit spheres may allow a center sphere to bulge out.
227. Regular Antiprism:  Height and volume of a regular n-gonal antiprism.
228. The Szilassi polyhedron  features 7 pairwise adjacent hexagonal faces.
229. Wooden buckyball:  Cutting 32 blocks to make a truncated icosahedron.

     Graph Theory

230. The bridges of Königsberg:  Eulerian graphs  and the birth of  graph theory.
231. Undirected graphs are digraphs with  symmetrical  adjacency matrix.
232. Adjacency matrix of a directed graph  (digraph)  or of a  bipartite graph.
233. Silent Circles:  An enumeration based on adjacency matrices  (Max Alekseyev).
234. Silent Prisms:  Another version of the screaming game, for short-sighted people.
235. Tallying  all markings of one edge per node in which no edge is marked twice.
236. Line graph:  The nodes of L(G) are edges of G  (connected  iff  adjacent in G).
237. Transitivity:  Vertex-transitive and/or edge-transitive graphs.

     Algebra

238. Factorial zero is 1, so is an empty product; an empty sum is 0.
239. Anything raised to the power of 0 is equal to 1, including 0 to the power of 0.
240. Idiot's Guide to Complex Numbers.
241. Using the Golden Ratio (f) to express the 5 [complex] fifth roots of unity.
242. "Multivalued" functions are functions defined over a Riemann surface.
243. Square roots are inherently ambiguous for negative or complex numbers.
244. The difference of two numbers, given their sum and their product.
245. Symmetric polynomials of 3 variables: Obtain the value of one from 3 others.
246. Geometric progression of 6 terms. Sum is 14, sum of squares is 133.
247. Quartic equation involved in the classic "Ladders in an Alley" problem.

     Matrices and Determinants

248. Permutation matrices  include the identity matrix and the exchange matrix.
249. Operations on matrices  are conveniently defined using  Dirac's notation.
250. Vandermonde matrix:  The successive powers of elements in its second row.
251. Toeplitz matrix:  Constant diagonals.
252. Circulant matrix:  Cyclic permutations of the first row.
253. Wendt's Determinant:  The circulant of the binomial coefficients.
254. Hankel matrix:  Constant skew-diagonals.
255. Catberg matrix:  Hankel matrix of the reciprocal of Catalan numbers.
256. Hadamard matrix:  Unit elements and orthogonal columns.
257. Sylvester matrix  of two polynomials has their resultant for determinant.
258. The discriminant of a polynomial is the resultant of itself and its derivative.

     Trigonometry, Elementary Functions, Special Functions

259. Numerical functions: Polynomial, rational, algebraic, transcendental, special...
260. Trigonometric functions:  Memorize a simple picture for 3 basic definitions.
261. Solving triangles with the law of sines, law of cosines, and law of tangents.
262. Spherical trigonometry:  Triangles drawn on the surface of a sphere.
263. Sum of tangents of two half angles, in terms of sums of sines and cosines.
264. The absolute value of the sine of a complex number.
265. Exact solutions to transcendental equations.
266. All positive rationals (and their square roots) as trigonometric functions of zero!
267. The sine function: How to compute it numerically.
268. Chebyshev economization saves billions of operations on routine computations.
269. The Gamma function: Its definition(s) properties and values.
270. Lambert's W function is used to solve practical transcendental equations.

     Hypergeometric Functions

271. Pochhammer's symbol:  Upper factorial of k increasing factors, starting with x.
272. Gauss's hypergeometric function:  2+1 parameters (and one variable).
273. Kummer's transformations relate different values of the hypergeometric function.
274. Sum of the reciprocal of Catalan numbers, in closed hypergeometric form.

     Calculus

275. Derivative: Usually, the slope of a function, but there's a more abstract approach.
276. Integration: The Fundamental Theorem of Calculus.
277. 0 to 60 mph in 4.59 s, may not always mean 201.96 feet.
278. Integration by parts:  Reducing an integral to another one.
279. Length of a parabolic arc.
280. Top height of a curved bridge spanning a mile, if its length is just a foot longer.
281. Sagging:  A cable which spans 28 m and sags 30 cm is 28.00857 m long.
282. The length of the arch of a cycloid is 4 times the diameter of the wheel.
283. Integrating the cube root of the tangent function.
284. Changing inclination to a particle moving along a parabola.
285. Algebraic area of a "figure 8" may be the sum or the difference of its lobes.
286. Area surrounded by an oriented planar loop  which  may  intersect itself.
287. Linear differential equations of higher order and/or in several variables.
288. Theory of Distributions:  Convolution products and their usage.
289. Laplace Transforms: The Operational Calculus of Oliver Heaviside.
290. Integrability of a function and of its absolute value.
291. Analytic functions of a linear operator; defining  f (D) when D is d/dx...

     Differential Equations

292. Ordinary differential equations. Several examples.
293. A singular change of variable  is valid over a domain which may not be maximal.
294. Vertical fall  against fluid resistance  (including both viscous and quadratic drag).

     Differential Forms  &  Vector Calculus

295. Generalizing the  fundamental theorem of calculus.
296. The surface of a loop  is a vector determining its apparent area in any direction.
297. Practical identities  of vector calculus

     Optimization:  Operations Research, Calculus of Variations

298. Stationary points  (or  saddlepoints )  are where  all  partial derivatives vanish.
299. Single-variable optimization:  Derivative vanishes unless the variable is extreme.
300. Extrema of a function of two variables  must satisfy a  second-order  condition.
301. Saddlepoints of a multivariate function.  One equation to satisfy per variable.
302. Lagrange multipliers:  Optimizing an objective function under various constraints.
303. Minimizing the lateral surface area of a cone  of given base and volume.
304. Euler-Lagrange equations  hold along the path of a  stationary  integral.
305. Noether's theorem:  A symmetry of the integrand yields a conserved quantity.
306. Isoperimetric Inequality:  The largest area enclosed by a loop of unit perimeter.
307. Plateau's problem  extends the calculus of variations from paths to membranes.
308. Embedded minimal surfaces: Plane, catenoid, helicoid, Costa's surface, etc.
309. Connecting blue dots to red dots  in the plane, without any crossings...
310. The shortest way to connect 3 dots  can be to join them to a  fourth  point.
311. The Honeycomb Theorem:  A conjecture of old, proved by  Thomas Hales.
312. Counterexamples to Kelvin's conjecture.  Tiling space with unit cells of least area.

     Analysis, Convergence, Series, Complex Analysis

313. Cauchy sequences help define real numbers rigorously.
314. Permuting the terms of a series may change its sum arbitrarily.
315. Uniform convergence implies properties for the limit of a sequence of functions.
316. Defining integrals: Cauchy, Riemann, Darboux, Lebesgue.
317. Cauchy principal value of an integral.
318. Fourier series. A simple example.
319. Infinite sums may sometimes be evaluated with Fourier Series.
320. A double sum is often the product of two sums, which may be Fourier series.
321. At a jump, the sum of a Fourier series is the half-sum of its left and right limits.
322. Gibbs phenomenon; 9% overshoot of partial Fourier series near a jump.
323. Method of Froebenius about a regular singularity of a differential equation.
324. Laurent series of a function about one of its poles.
325. Cauchy's Residue Theorem is helpful to compute difficult definite integrals.
326. Tame complex functions: Holomorphic and meromorphic functions.

     Complex Power Series  &  Analytic Continuations

327. Radius of convergence.  The convergence disk of a complex power series.
328. Analytic continuation:  Power series that coincide whenever their disks overlap.
329. Decimated power series are equal to finite sums involving  roots of unity.

     Fourier Transform  &  Tempered Distributions

330. Convolution  as an inner operation among numerical functions.
331. Duality:  The product of a  bra  by a  ket  is a (complex) scalar.
332. A  distribution  associates a scalar to every  test function.
333. Schwartz functions  are suitable  rapidly decreasing  test functions.
334. Tempered distributions  are functionals over Schwartz functions.
335. The Fourier Transform  associates a  tempered distribution  to another.
336. Parseval's theorem  (1799).  The Fourier transform is unitary.
337. Noteworthy distributions and their Fourier transforms: 
     • Dirac's  d  and the  uniform  distribution  ( f (x) = 1).
     • The  signum  function  sign(x)  and its transform:   i / ps
     • The Heaviside step function  H(x) = ½ (1+sign(x))  and its transform.
     • The square function  P(x) = H(x+½)-H(x-½)   and   sinc ( ps )
     • The triangle function  L(x)   and   sinc² ( ps )
     • The normalized Gaussian distribution is its own Fourier transform.
338. Poisson summation formula:  The unit comb  ()  is its own Fourier transform.
339. Far image of a translucent film  is the Fourier transform of its optical density.
340. The Radon transform, corresponding to lateral tomography, is easily inverted.
341. Competing definitions of the Fourier transform.  For the record.

     Discrete Fourier Transforms  &  Fast Fourier Transform

342. Discrete Fourier Transform,  defined as a  unitary involution.

     Set Theory and Logic

343. The Barber's Dilemma. Not a paradox if analyzed properly.
344. What is infinity? More than a pretty symbol (¥).
345. There are more real than rational numbers. Cantor's argument.
346. Cantor's ternary set.  A vanishing set or reals  equipollent  to the whole line.
347. The axioms of set theory: Fundamental axioms and the Axiom of Choice.
348. A set is smaller than its powerset:  A simple proof applies to all sets.
349. Transfinite cardinals, transfinite ordinals: Two different kinds of infinite numbers.
350. The continuum hypothesis:  What's between the countable and the continuum?
351. Surreal Numbers:  These include reals, transfinite ordinals, infinitesimals & more.
352. Numbers:  From integers to surreals.  From reals to quaternions and  beyond.

     Integer Arithmetic, Number Theory

353. The number 1 is not prime, as definitions are chosen to make theorems simple.
354. Composite numbers are not prime, but the converse need not be true...
355. Two prime numbers whose sum is equal to their product.
356. Gaussian integers:  Factoring into primes on a two-dimensional grid.
357. The least common multiple may be obtained without factoring into primes.
358. Standard Factorizations:   n⁴ + 4   is never prime for   n > 1   because...
359. Euclid's algorithm gives the greatest common divisor and Bézout coefficients.
360. Bézout's Theorem:  The GCD of p and q is of the form  u p + v q.
361. Greatest Common Divisor  (GCD)  defined for all commensurable numbers.
362. Linear equation in integers  can be solved using  Bézout's theorem.
363. Pythagorean Triples:  Right triangles whose sides are coprime integers.
364. The number of divisors of an integer.
365. Perfect squares are the only integers with an odd number of positive divisors.
366. Perfect numbers and Mersenne primes.
367. Multiperfect and hemiperfect numbers  divide  twice the sum of their divisors.
368. Fast exponentiation by repeated squaring.
369. Partition function. How many collections of positive integers add up to 15?
370. A Lucas sequence whose oscillations never carry it back to -1.
371. A bit sequence  with intriguing statistics.  Counting squares between cubes.
372. Binet's formulas: N-th term of a sequence obeying a second-order recurrence.
373. The square of a Fibonacci number  is  almost  the product of its neighbors.
374. D'Ocagne's identity  relates conjugates products of Fibonacci numbers.
375. Catalans's identity  generalizes  Cassini's Identity  (about Fibonacci squares).
376. Faulhaber's formula gives the sum of the p-th powers of the first n integers.
377. Multiplicative functions:  If a and b are  coprime, then  f(ab) =  f(a) f(b).
378. Moebius function:  Getting  N  values with only  O(N Log(Log N))  additions.
379. Dirichlet convolution is especially interesting for  multiplicative  functions.
380. Dirichlet powers of arithmetic functions  (especially, of the Moebius function).
381. Dirichlet powers of multiplicative functions  are given by a  superb formula.
382. Totally multiplicative functions are the simplest type of multiplicative functions.
383. Dirichlet characters are important  totally multiplicative functions.
384. Euler products  and generalized zeta functions.

     Positional Numeration  &  Number Systems

385. Modular Arithmetic may be used to find the last digit(s) of very large numbers.
386. Powers of ten expressed as products of two factors  without zero digits.
387. Divisibility by 7, 13, and 91 (or by B²-B+1 in base B).
388. Lucky 7's.  Any integer divides a number composed of only 7's and 0's.
389. Binary and/or hexadecimal numeration for floating-point numbers as well.
390. Extract a square root the old-fashioned way.
391. Ternary system:  Is base 3  really  the best radix for positional numeration?

     Prime Numbers

392. A prime number  is a positive integer with just two distinct divisors (1 and itself).
393. Euclid's proof:  There are infinitely many primes.
394. Dirichlet's theorem:  There are infinitely many primes of the form  kN+a.
395. Green-Tao theorem:  There are arbitrarily long arithmetic progressions of primes.
396. The von Mangoldt function  is  Log p  for a power of a prime p,  0 otherwise.
397. The Prime Number Theorem:  The probability that N is prime is roughly 1/ln(N).
398. The average number of factors  of a large number  N  is  Log N.
399. The average number of distinct prime factors  of  N  is  Log Log N.
400. The largest known prime:  Historical records, old and new.
401. The Lucas-Lehmer Test  checks the primality of a Mersenne number  very fast.
402. Formulas giving only primes  may not help with new primes.
403. Ulam's Lucky Numbers  and other sequences generated by sieves.

     Modular Arithmetic

404. Chinese Remainder Theorem:  How remainders define an integer (within limits).
405. Modular arithmetic: The algebra of congruences, formally introduced by Gauss.
406. Fermat's little theorem:   For any prime p, a^p-1 is 1 modulo p, unless p divides a.
407. Euler's totient function:  f(n) is the number of integers coprime to n, from 1 to n.
408. Fermat-Euler theorem:  If  a is coprime to n,  then a to the  f(n)  is 1 modulo n.
409. Carmichael's reduced totient function (l) : A very special divisor of the totient.
410. 91 is a pseudoprime to half of the bases coprime to itself.
411. Carmichael Numbers:  An absolute pseudoprime  n divides  (aⁿ - a)  for any a.
412. Chernik's Carmichael numbers:  3 prime factors   (6k+1)(12k+1)(18k+1).
413. Large Carmichael numbers may be obtained in various ways.
414. Conjecture: Any odd number coprime to its totient has a Carmichael multiple.

     Group Theory and Symmetries

415. Monoids  are endowed with an  associative  operation and a  neutral element.
416. The inverse of an element  comes in two flavors which coincide when both exist.
417. Free monoid:  All the finite strings (words) in a given  alphabet.
418. Groups  are monoids in which  every element  is invertible.
419. A subgroup is a group  contained in another group.
420. Generators  of a group are not contained in any  proper  subgroup.
421. Lagrange's Theorem:  The order of a subgroup divides the order of the group.
422. Normal subgroups  and their quotients in a group.
423. Group homomorphism:  The image of a product is the product of the images.
424. The symmetric group  on a set E consists of all the bijections of E onto itself.
425. Inner automorphisms:  Inn(G)  is isomorphic to the quotient of  G  by its center.
426. The conjugacy class formula  uses conjugacy to tally elements of a group.
427. Simple groups  are groups without  nontrivial  normal subgroups.
428. The derived subgroup  of a group is  generated  by its  commutators.
429. Direct product of two groups  (also called a  direct sum  for additive groups).
430. Groups of small orders  and their families:  Cyclic groups, dihedral groups, etc.
431. Enumeration  of "small" groups.  How many groups of order n?
432. Classification of finite simple groups,  by Gorenstein and many others (1982).
433. Sporadic groups:  Tits Group, 20 relatives of Fischer's Monster, 6 pariahs.
434. Classical groups:  Their elements depend on parameters from a  field.
435. The Möbius group  consists of homographic transformations of  È{¥}.
436. Lorentz transformations  may  change spatial orientation or time direction.
437. Symmetries of the laws of nature:  A short primer.

     Ring Theory

438. Rings  are sets endowed with addition, subtraction and multiplication.
439. Nonzero characteristic:  The least  p  for which all sums of  p  like terms vanish.
440. Ideals  within a ring are  multiplicatively absorbent  additive subgroups.
441. Quotient ring, modulo an ideal:  The residue classes modulo that ideal.
442. Cauchy multiplication  is well-defined for "formal power series" over a ring.
443. Ring of polynomials  whose coefficients are in a given ring.
444. Galois rings.  Residues of modular polynomials,  modulo  one of them.

     Fields, Galois Fields and Skew Fields

445. Vocabulary:  We consider  skew fields  to be  noncommutative.  Some don't.
446. Fields  are commutative rings where every nonzero element has a reciprocal.
447. Wedderburn's Theorem:  Finite  division rings are commutative  (they're fields).
448. Every  finite  integral domain is a field.  A corollary of  Wedderburn's theorem.
449. Galois fields  are the  finite fields.  Their orders are powers of prime numbers.
450. The trivial field  has a single element.  It's the only field where 0 has a reciprocal.
451. The splitting field  of PÎF[x]  is the smallest extension of F where P fully factors.
452. The Nim-Field  is algebraically complete.  It contains [surreal] infinite ordinals.
453. Ternary multiplication  compatible with  ternary addition  (without "carry").

     Vector Spaces  (over a field)  and  Modules  (over a ring)

454. Vectors  were originally just differences between points in ordinary space...
455. Abstract vector spaces:  Vectors can be added, subtracted and  scaled.
456. Modules  are vectorial structures over a  ring of scalars  (instead of a  field).
457. Banach spaces  are  complete  normed vector spaces.
458. Dual space:  The set of all [continuous] linear functions with scalar values.
459. Tensors:  Multilinear functions of vectors and covectors with scalar values.
460. An algebra  is a vector space with a scalable and distributive internal product.
461. Clifford algebras are unital associative algebras endowed with a quadratic form.
462. Physical things that are not vectorial  because they're not defined  intrinsically.
463. David Hestenes has proposed  geometric algebra  as a denotational unification.

     Ring of p-adic Integers, Field of p-adic Numbers

464. The ring of p-adic integers  includes objects with infinitely many radix-p digits.
465. Polyadic integers:  Greek naming of p-adic integers.
466. What if p isn't prime?  Dealing with  divisors of zero.
467. Decadic Integers:  The strange realm of 10-adic integers  (composite radix).
468. The field of p-adic numbers  is the  quotient field  of the ring of p-adic integers.
469. Dividing two p-adic numbers  looks like "long division", only backwards...
470. The p-adic metric can be used to define p-adic numbers analytically.
471. The reciprocal of a p-adic number  computed by successive approximations.
472. Hasse's local-global principle  was established for the quadratic case in 1920.
473. Integers which double  when their digits (in base g) are rotated.

     Pseudoprimes

474. Pseudoprimes to base a.  Poulet numbers  are pseudoprimes to base 2.
475. Weak pseudoprimes to base a :  Composite integers  n  which divide  (aⁿ-a).
476. Counting the bases  to which a composite number is a pseudoprime.
477. Strong pseudoprimes to base a  are less common than Euler pseudoprimes.
478. Rabin-Miller Test:  An efficient and trustworthy  stochastic  primality test.
479. The product of 3 primes  is a pseudoprime when all  pairwise  products are.
480. Wieferich primes  are scarce but there are (probably) infinitely many of them.
481. Super-pseudoprimes:  All  their composite divisors are pseudoprimes.
482. Maximal super-pseudoprimes  have no super-pseudoprime multiples.

     Factoring into Primes

483. Jevons Number.  Factoring  8616460799  is now an  easy  task.
484. Challenges  help tell  special-purpose  and  general-purpose  methods apart.
485. Special cases  of  a priori  (partial) factorizations may help number theorists.
486. Trial division  may be used to weed out the small prime factors of a number.
487. Ruling out factors  can speed up trial divison in special cases.
488. Recursively defined sequences  (over a  finite  set)  are  ultimately periodic.
489. Pollard's r (rho) factoring method  is based on the properties of such sequences.
490. Pollard's p-1 Method  finds prime factors  p  for which  p-1  is  smooth.
491. Williams' p+1 Method  is based on the properties of Lucas sequences.
492. Lenstra's Elliptic Curve Method  is a generalization of Pollard's p-1 approach.
493. Dixon's method:  Combine small square residues into a solution of   x ² º y ²

     Quadratic Reciprocity

494. Motivation:  On the prime factors of some quadratic forms...
495. Quadratic residues:  Half of the nonzero residues modulo an odd prime  p.
496. Euler's criterion:  A quadratic residue raised to the power of  (p-1)/2  is 1.
497. The Legendre symbol  (a|p)  can be extended to values of p besides odd primes.
498. The law of quadratic reciprocity  states a simple but surprising fact.
499. Gauss' Lemma  expresses a  Legendre symbol  as a product of many  signs.
500. Eisenstein's Lemma:  A variation of  Gauss's lemma  allowing a simpler proof.
501. One of many proofs of the  law of quadratic reciprocity.
502. Artin's Reciprocity.

     Continued Fractions  (and related topics)

503. What is a continued fraction?  Example:  The expansion of p.
504. The convergents of a number are its best rational approximations.
505. Large partial quotients allow very precise approximations.
506. Regular patterns in the continued fractions of some irrational numbers.
507. For almost all numbers, partial quotients are ≥ k with probability  lg(1+1/k).
508. Elementary operations on continued fractions.
509. Expanding functions as continued fractions.
510. Engel expansion of a positive number.  A nondecreasing sequence of integers.
511. Pierce expansions of numbers between 0 and 1.  Strictly increasing sequences.

     Recreational Mathematics

512. Counterfeit Coin Problem: In 3 weighings, find an odd object among 12, 13, 14.
     • Unabridged discussion.
513. General Counterfeit Penny Problem: Find an odd object in the fewest weighings.
     • Unabridged discussion.
514. Seven-Eleven: Four prices with a sum and product both equal to 7.11.
515. Equating a right angle and an obtuse angle, with a clever false proof.
516. Choosing a raise: Trust common sense, beware of  fallacious accounting.
517. 3 men pay $30 for a $25 hotel room, the bellhop keeps $2... Is $1 missing?
518. Chameleons: A situation shown unreachable because of an invariant quantity.
519. Sam Loyd's 14-15 puzzle also involves an invariant quantity (and two orbits).
520. Einstein's riddle: 5 distinct house colors, nationalities, drinks, smokes and pets.
521. Numbering n pages of a book takes this many digits (formula).
522. The Ferry Boat Problem (by Sam Loyd): To be or not to be ingenious?
523. Hat overboard !   What's the speed of the river?
524. All digits once and only once: 48 possible sums (or 22 products).
525. Crossing a bridge: 1 or 2 at a time, 4 people (U2), different paces, one flashlight!
526. Managing supplies to reach an outpost 6 days away, carrying enough for 4 days.
527. Go south, east, north and you're back... not necessarily to the North Pole!
528. Icosapolis: Numbering a 5 by 4 grid so adjacent numbers differ by at least 4.
529. Unusual mathematical boast for people born in 1806, 1892, or 1980.
530. Puzzles for extra credit: From Chinese remainders to the Bookworm Classic.
531. Simple geometrical dissection:  A proof of the Pythagorean theorem.
532. Early bird saves time by walking to meet incoming chauffeur.
533. Sharing a meal: A man has 2 loaves, the other has 3, a stranger has 5 coins.
534. Fork in the road: Find the way to Heaven by asking only one question.

     ---

535. Proverbial Numbers: Guess the words which commonly describe many numbers.
536. Riddles: The Riddle of the Sphinx and other classics, old and new.

     The Mathematical Games of Martin Gardner

537. Flexagons:  Hexaflexagons  were popularized by Martin Gardner in 1956.
538. Polyominoes:  The 12 pentominoes and other tiles invented by  Sol Golomb.
539. Soma:  7 nonconvex solids consisting of  3 or 4  cubes make a larger cube.
540. Tessellations by convex pentagons.  The contributions of  Marjorie Rice.
541. Kites and Darts.  The  aperiodic  tilings of Roger Penrose.
542. Ambigrams:  Calligraphic spellings which change when rotated or flipped.
543. The Game of Life.  John Conway's  endearing  cellular automaton  (1970).
544. Rubik's Cube:  Ernõ Rubik (1974)  D. Singmaster (1979)  M. Gardner (1981).

     Mathematical "Magic" Tricks

545. 1089:  Subtract a 3-digit number and its reverse, then add this to  its  reverse...
546. Mass media mentalism  by  David Copperfield  (1992).
547. Grey Elephants in Denmark: "Mental magic" for one-time classroom use.
548. The 5-card trick of Fitch Cheney:  Tell the fifth card once 4 are known.
549. Generalizing the 5-card trick and  Devil's Poker...
550. Kruskal's Count.
551. Paths to God.
552. Stacked Deck.
553. Magic Age Cards.
554. Ternary Cards.
555. Magical 21  (or 27).
556. Boolean Magic.
557. Perfect Faro Shuffles.

     Mathematical Games (Strategies)

558. Dots and Boxes: The "Boxer's Puzzle" position of Sam Loyd.
559. The Game of Nim: Remove items from one of several rows. Don't play last.
560. Grundy numbers are defined for all positions in impartial games.
561. Moore's Nim: Remove something from at most (b-1) rows. Play last.
562. Normal Kayles: Knocking down one pin, or two adjacent ones, may split a row.
563. Grundy's Game: Split a row into two unequal rows. Whoever can't move loses.
564. Wythoff's Game: Remove counters either from one heap or equally from both.

     The Game of Chess

565. Nalimov Tables:  Perfect analysis of endgame situations.
566. Evaluation function:  Estimating a quiescent position statically.
567. Minimax search tree:  The basic paradigm for analyzing two-player games.
568. Alpha-beta pruning.  Iin a minimax search, some alternatives can be ignored.
569. Hash tables.  How to avoid analyzing the same position more than once.
570. Short chess games.  Checkmates occuring during the opening moves.
571. Classic traps:  Fishing pole, etc.

     Ramsey Theory

572. The pigeonhole principle:  What must happen with fewer holes than pigeons...
573. n+1 of the first 2n integers  always include two which are coprime.
574. Largest sets of small numbers with at most  k  pairwise coprime integers.
575. Ramsey's Theorem:  Monochromatic complete subgraphs of a large graph.
576. Infinite alignment among infinitely many lattice points in the plane?  Nope.
577. Infinite alignment in a lattice sequence with bounded gaps?  Almost...
578. Large alignments in a lattice sequence with bounded gaps.  Yeah!
579. Van der Waerden's theorem:  Long monochromatic arithmetic progressions.

     Miscellaneous

580. Ford circles are nonintersecting circles touching the real line at rational points.
581. Farey series:  The rationals from 0 to 1, with a bounded denominator.
582. The Stern-Brocot tree  contains a single occurrence of every positive rational.
583. Any positive rational  is a unique ratio of two consecutive Stern numbers.
584. Pick's formula gives the area of a lattice polygon by counting lattice points.

     History, Nomenclature, Vocabulary, etc.

     History :
585. Earliest mathematics on record. Before Thales was Euphorbe...
586. Indian numeration became a positional system with the introduction of zero.
587. Roman numerals are awkward for larger numbers.
     • Roman numerals: Unabridged discussion.
588. The invention of logarithms: John Napier, Bürgi, Briggs, Saint-Vincent, Euler.
589. The earliest mechanical calculator(s), by W. Shickard (1623) or Pascal (1642).
590. The Fahrenheit Scale: 100°F  was meant to be the normal body temperature.
591. The revolutionary innovations  which brought about new civilizations.
     Nomenclature & Etymology :
592. The origin of the word "algebra", and also that of "algorithm".
593. The name of the avoirdupois system:  Borrowed from French in a pristine form.
594. Long Division: Cultural differences in writing the details of a division process.
595. Is a parallelogram a trapezoid? In a mathematical context [only?], yes it is...
596. Naming polygons. Greek only please; use hendecagon not "undecagon".
597. Chemical nomenclature: Basic sequential names (systematic and/or traditional).
598. Fractional Prefixes: hemi (1/2), sesqui (3/2) or weirder hemipenta, hemisesqui...
     • Matches, phosphorus, and phosphorus sesquisulphide.
599. Zillion. Naming large numbers.
600. Zillionplex. Naming huge numbers.

     Style and Usage

601. Abbreviations:  Abbreviations of scholarly Latin expressions.
602. Typography of long numbers.
603. Intervals  denoted with square brackets (outward for an excluded extremity).
604. Dates  in the simplest ISO 8601 form  (with  customary  time stamps or not).
605. The names of operands in common numerical operations.
606. The word  respectively  doesn't have the same syntax as "resp."

     Setting the Record Straight

607. The heliocentric Copernican system was known two millenia before Copernicus.
608. The assistants of Galileo Galilei and the mythical experiment at the Tower of Pisa.
609. Switching calendars: Newton was not born the year Galileo died.
610. The Lorenz Gauge is an idea of Ludwig Lorenz (1829-1891) not H.A. Lorentz.
611. Special Relativity was first formulated by H. Poincaré (Einstein a close second).
612. The Fletcher-Millikan "oil-drop" experiment was not the sole work of Millikan.
613. Collected errata  about customary physical units.
614. Portrait of Legendre:  The  mathematician  was confused with the politician.
615. Dubious quotations:  Who  really  said that?

     Ancient Knowledge

616. Classical geometry  describes an  homogeneous  space indifferent to scale.
617. Obliquity of the ecliptic:  An evolving quantity first measured by Eratosthenes.
618. Vertical wells at Syene are completely sunlit only once a year, aren't they?
619. Eratosthenes sizes up the Earth:  700 stadia per degree of latitude.
620. Latitude and longitude:  The spherical grid of meridians and parallels.
621. Itinerary units:  The  land league  and the  nautical league.
622. Amber, compass and lightning:  Glimpses of electricity and magnetism.

     Physics

623. The "work done" on a point-mass  equals the change in its  kinetic energy.
624. Relativistic work done  and the corresponding change in  relativistic energy.
625. Relativistic thermodynamics:  The case of a point endowed with internal heat.
626. Spacecraft speeds up upon reentry into the upper atmosphere.
627. Lewis Carroll's monkey climbs a rope over a pulley, with a counterweight.
628. Two-ball drop can make a light ball bounce up to 9 times the dropping height.
629. Normal acceleration  is the square of speed divided by the radius of curvature.
630. Roller-coasters  must rise more than half a radius above any  loop-the-loop.
631. Conical pendulum:  A hanging bob whose trajectory is an horizontal circle.
632. Ball in a Bowl:  Pure rolling  increases the period of oscillation by 18.3%.
633. Hooke's Law:  Motion of a mass suspended to a spring.
634. Speed of an electron estimated with the Bohr model of the atom.
635. Thermal expansion coefficients:  The cubical coefficient is 3 times the linear one.
636. Waves in a solid: P-waves (fastest), S-waves, E-waves (thin rod), SAW...
637. Rayleigh Wave: The quintessential surface acoustic wave (SAW).
638. Hardest Stuff:  Diamond is no longer the hardest material known to science.
639. Hardness  is an elusive  nonelastic  property, distinct from  stiffness.
640. Hot summers, hot equator! The distance to the Sun is not the explanation.
641. Kelvin's Thunderstorm:  Using falling water drops to generate high voltages.
642. The Coriolis effect:  A dropped object falls to the east of the plumb line.
643. Terminal velocity  of an object falling in the air.
644. Angular momentum and torque.  Spin and orbital angular momentum.

     Motion of Rigid Bodies  (Classical Mechanics)

645. Rotation vector  of a moving rigid body (and/or "frame of reference").
646. Angular momentum  equals  moment of inertia  times  angular velocity.
647. Moments about a point or a plane  are convenient mathematical fictions.
648. Moment of inertia of a spherical distribution  and of an homogeneous ellipsoid.
649. Perpendicular Axis Theorem:  Axis of rotation perpendicular to a  thin plate.
650. The Parallel Axis Theorem  gives the moment of inertia about an off-center axis.
651. Moment of inertia of a thick plate,  as obtained from the  parallel axis theorem.
652. Momenta of homogeneous bodies:  List of examples.
653. Rigid pendulum  moving under its own weight about a fixed horizontal axis.
654. Reversible pendulum  swings with the same period around two distinct axes.

     Newtonian Gravity

655. All physical theories  have a limited range of validity.
656. Gravity vs. Electrostatics:  Straight comparisons.
657. Airy weighs the Earth  by timing a pendulum at the bottom of a mine.
658. Rigid equilateral triangle  formed by three gravitating bodies.
659. The five Lagrange points  of two gravitating bodies in circular orbit.

     Waves

660. Huygens' Principle  is a convenient fiction to describe the propagation of waves.
661. Diffraction  occurs when when a wave emanates from a bounded source.
662. Young's  double-slit  experiment  demonstrates the wavelike nature of light.
663. Celerity  is the speed with which  phase  propagates.
664. Standing waves  feature stationary nodes and antinodes.
665. Chladni patterns:  The lines formed by nodes in an oscillating  plate  (or surface).
666. Snell's Law (1621)  gives the angle of refraction (or says nothing is refracted).
667. Birefringence  and the discovery of  polarization  (Erasmus Bartholinus, 1669).
668. Brewster's angle  is the incidence which yields a 100% polarized reflection.
669. Fresnel equations  give the reflected or refracted intensities of polarized light.
670. Stokes parameters:  A standard description of the  state of polarization.

     Colors & Dispersion

671. Dispersion relation:  pulsatance vs. wave number (or frequency vs. wavelength).
672. Group velocity  is the traveling speed of a beat phenomenon.
673. Rayleigh scattering  makes the sky blue and sunsets red.
674. Index of refraction of water  for light of different colors.
675. A spherical drop  bounces red light up to 42.34° and violet light up to 40.58°.
676. The  length  of a rainbow  (mathematical digression).

     Analytical Mechanics  &  Classical Field Theory

677. Fermat's principle  (least time)  for light (c.1655) predates Newton's mechanics.
678. Maupertuis principle  of  least action  (1744).
679. Virtual Work:  A substitute for Newton's laws which factors out constraint forces.
680. Phase Space:  A   phase  describes all there is to a classical system.
681. Either velocities or momenta  can be used (with positions) to specify a  phase.
682. Relativistic point-mass:  Lagrangian, Hamiltonian and momentum in free space.
683. Charge in a magnetic field:  The canonical momentum isn't the linear momentum.
684. Lagrangian mechanics:  The  Lagrangian  is a function of positions and velocities.
685. Hamiltonian mechanics:  The  Hamiltonian  depends on positions and momenta.
686. Poisson brackets:  An abstract synthetic view of analytical mechanics.
687. Liouville's theorem:  The  volume  in Hamiltonian phase space doesn't change.
688. Noether's Theorem:  Conservation laws express the symmetries of physics.
689. Field Theory:  Lagrangian mechanics on a continuum of values (and derivatives).

     Electromagnetism  (Maxwell's Equations)

690. Clarifications by Heaviside & Lorentz:  Vector calculus & microscopic view.
691. The vexing problem of units  is a thing of the past if you stick to SI units.
692. The Lorentz force  on a test particle defines the local electromagnetic fields.
693. Electrostatics:  The study of the electric field due to static charges.
694. Electric capacity  is an electrostatic concept  (adequate at low frequencies).
695. Electrostatic multipoles:  The multipole expansion of an electrostatic field.
696. Birth of electromagnetism (1820):  Electric currents generate magnetic fields !
697. Biot-Savart Law:  The  static  magnetic induction due to steady currents.
698. Magnetic scalar potential:  A multivalued function whose gradient is induction.
699. Magnetic monopoles do not exist :  A law stating a fact not yet disproved.
700. Ampère's law:  The law of static electromagnetism devised by Ampère in 1825.
701. Faraday's law:  A varying magnetic flux  induces  an electric circulation.
702. Self-induction:  The induction received by a circuit from its own magnetic field.
703. Ampère-Maxwell law:  The dynamic generalization (1861) of  Ampère's law.
704. Putting it all together:  Historical paths to Maxwell's  electromagnetism.
705. Maxwell's equations  unify electricity and magnetism dynamically  (1864).
706. Continuity equation:  Maxwell's equations imply  conservation of charge.
707. Waves anticipated by Faraday, Maxwell & FitzGerald were observed by Hertz.
708. Electromagnetic energy density  and the flux of the Poynting vector.
709. Planar electromagnetic waves:  The simplest type of electromagnetic waves.
710. Maxwell-Bartoli radiation pressure.  Demonstrated experimentally by Lebedev.
711. Electromagnetic potentials  are postulated to obey the  Lorenz gauge.
712. Solutions to Maxwell's equations,  as  retarded  or  advanced  potentials.
713. Electrodynamic fields  corresponding to  retarded  potentials.
714. The gauge of retarded potentials:  is it  really  the Lorenz gauge?
715. Electric and magnetic dipoles:  Dipolar solutions of Maxwell's equations.
716. Static distributions of magnetic dipoles  can be simulated with steady currents.
717. Static distributions of electric dipoles  can be simulated with static charges.
718. Sign reversal  in the fields of uniformly distributed magnetic or electric dipoles.
719. Fields at the center of uniformly magnetized or polarized spheres  (of any size).
720. Relativistic dipoles:  A moving magnet develops an electric moment.
721. Power radiated by an accelerated charge:  The Larmor formula (1897).
722. Lorentz-Dirac equation  for the motion of a point charge is of  third  order.

     Electromagnetic Dipoles

723. Molecular electric dipole moments  were first studied by Peter Debye (1912).
724. Force exerted on a dipole  by a  nonuniform  field.
725. Torque on a dipole  is proportional to its cross-product into the field.

     Magnetism,  Electromagnetic Properties of Matter

726. Magnetization and polarization  describe densities of dipoles  bound  to matter.
727. Gauge invariance:  Many magnetizations and polarizations create the same field.
728. Maxwell's equations in matter:  Electric displacement D,  magnetic strength H.
729. Electric susceptibility  is the propensity to be polarized by an  electric field.
730. Electric permittivity and magnetic permeability  are related to susceptibilities.
731. Paramagnetism:  Weak  positive  susceptibility.
732. Diamagnetism:  The Lorentz force turns orbital moments against the external B.
733. Magnetic levitation:  How to skirt the theorem of Samuel Earnshaw (1842).
734. Pyrolytic carbon:  The most diamagnetic sunstance known, at room temperature.
735. Bohr & Van Leeuwen Theorem:  Diamagnetism and paramagnetism cancel ?!
736. Thermodynamics of dielectric matter:  dU = E.dD + ...
737. Ferromagnetism:  Permanent magnetization without an external magnetic field.
738. Antiferromagnetism:  When adjacent dipoles tend to oppose each other...
739. Ferrimagnetism:  With two kinds of dipoles, partial cancellation may occur.
740. Magneto-optical effect  discovered by Faraday on September 13, 1845.
741. Ohm's Law:  Current density is proportional to electric field:  j = s E.

     Motors and Generators

742. Homopolar motor:  The first electric motor, by  Michael Faraday  (1831).
743. Faraday's disk  can generate huge currents at a low voltage.
744. Magic wheels:  Two repelling ring magnets mounted on the same axle.
745. Beakman's motor.  Current switches on and off as the coil spins horizontally.
746. Tesla turbine.  Stack of spinning disks with outer intake and inner outflow.

     Relativity

747. Observers in motion:  A simple-minded derivation of the Lorentz Transform.
748. Adding up velocities:  The combined speed can never be more than c.
749. Fizeau's empirical relation  between refractive index  (n) and  Fresnel drag.
750. The Harress-Sagnac effect  used to measure rotation with fiber optic cable.
751. Combining relativistic speeds:  Using rapidity, the rule is transparent.
752. Relative velocity of two photons:  Defined unless both have the same direction.
753. Minkowski spacetime:  Coordinates of 4-vectors obey the Lorentz transform.
754. The Lorentz transform expressed vectorially:  A so-called  boost  of speed  V.
755. Wave vector:  The 4-dimensional gradient of the phase describes propagation.
756. Doppler shift:  The relativistic effect is not purely radial.
757. Kinetic energy:  At low speed, the relativistic energy varies like  ½ mv ².
758. Photons and other massless particles:  Finite energy at speed  c.
759. The de Broglie celerity  (u)  is inversely proportional to a particle's speed.
760. Compton diffusion:  The result of collisions between photons and electrons.
761. The Klein-Nishina formula:  gives the  cross-section  in Compton scattering.
762. Compton effect is suppressed  quantically for visible light and bound electrons.
763. Elastic shock:  Energy transfer is  v.dp.  (None is seen from the barycenter.)
764. Photon-photon scattering  is like an  elastic collision of two photons.
765. Cherenkov Effect:  When the speed of an electron exceeds the celerity of light...
766. Constant acceleration  over an entire lifetime will take you  pretty far...

     General Relativity

767. The Harress-Sagnac effect  seen by an observer rotating with the optical loop.
768. Relativistic rigid motion  is an  equilibrium  modified at the speed of  sound.
769. In the Euclidean plane:  Contravariance and covariance.
770. In the Lorentzian plane:  Contravariance and covariance revisited.
771. Tensors of rank n+1  are linear maps that send a vector to a tensor of rank n.
772. Signature  of the quadratic form defined by a given metric tensor.
773. Covariant and contravariant coordinates  of tensors of rank  n, in 4 dimensions.
774. The metric tensor and its inverse.  Lowering and raising indices.
775. Partial derivatives  with respect to  contravariant  or  covariant  coordinates.
776. Christoffel symbols:  Coordinates of the partial derivatives of the basis vectors.
777. Covariant derivatives.  Absolute differentiation  with the  nabla  operator  Ñ.
778. Contravariant derivatives:  The lesser known flavor of absolute derivatives.
779. The antisymmetric part of Christoffels symbols  form a fundamental  tensor.
780. Totally antisymmetric spacetime torsion  is described by a  vector field.
781. Levi-Civita symbols:  Antisymmetric with respect to any pair of indices.
782. Einstein's equivalence principle  implies  vanishing  spacetime torsion.
783. Ricci's theorem:  The covariant derivative of the metric tensor vanishes.
784. Curvature:  The  Ricci tensor  is obtained by contracting the  Riemann tensor.
785. The Bianchi identity  show that the  Einstein tensor  is divergence free.
786. Stress tensor:  Flow of energy density is density of [conserved] momentum.
787. Einstein's Field Equations:  16 equations in covariant form (Einstein, 1915).
788. Free-falling bodies:  Their trajectories are  geodesics  in curved spacetime.
789. The "anomalous" precession of Mercury's perihelion  is entirely  relativistic.
790. The Schwarzschild metric:  The earliest exact solution to Einstein's equations.
791. What is mass?
792. Electromagnetism:  Covariant expressions, using tensors.
793. Kaluza-Klein theory of electromagnetism  involves a  fifth dimension.
794. Harvard Tower Experiment:  The slow clock at the bottom of the tower.
795. Shapiro time delay:  The effect on radar signals of gravitational time dilation.

     String Theory and other "Theories of Everything"

796. Unification:  Consistency is required.  Actual high-energy unification is not.
797. Kaluza-Klein Theory:  Postulating one extra dimension for electromagnetism.
798. Gabriele Veneziano:  The magic of Euler's  beta and gamma functions.
799. Leonard Susskind (1940-):  The basic idea of a fundamental string.
800. Joël Scherk (1946-1979) & John Schwarz:  Rediscovering  gravity.
801. Michael Green & John Schwarz:  Hoping for a  Theory of Everything.
802. String Quintet:  Five  different consistent string theories!
803. M-Theory:  Ed Witten's 11-dimensional brainchild, unveiled at  String '95.
804. The brane world scenarios  of  Lisa Randall  and  Burt Ovrut.

     Physics of Gases and Fluids

805. The Magdeburg hemispheres  are held together by more than one ton of force.
806. The ideal gas laws  of Boyle, Mariotte, Charles, Gay-Lussac, and Avogadro.
807. Joule's law:  The internal energy of a perfect gas depends only on its temperature.
808. The Van der Waals equation and other interesting equations of state.
809. Virial equation of state.  Virial expansion coefficients.  Boyle's temperature.
810. Viscosity is the ratio of a shear stress to the shear strain rate it induces.
811. Permeability and permeance: Vapor barriers and porous materials.
812. Resonant frequencies of air in a box.
813. The Earth's atmosphere. Pressure at sea-level and total mass above.
814. The first hot-air balloon  (Montgolfière)  was demonstrated on June 4, 1783.

     Transport Propertities of Matter

815. Viscosity:  The transport of microscopic momentum.
816. Brownian motion  and  Einstein's estimate of molecular sizes.
817. Thermal Conductivity:  The transport of microscopic energy.
818. Diffusivity: ration.
819. Speed of Sound:  Reversible transport of a pressure disturbance in a fluid.

     Filters and Feedback

820. Complex pulsatance (s)  is damping constant (s) plus imaginary pulsatance (iw).
821. Complex impedance:  Resistance and reactance.
822. Quality Factor (Q).  Ratio of maximal stored energy to dissipated power.
823. Nullators and norators:  Strange dipoles for analog electronic design.
824. Corner frequency  of a simple  first-order  low-pass filter.  -3 dB bandwidth.
825. Second-order  passive low-pass filter, with inductor and capacitor.
826. Sallen key filters:  Active filters do not require inductors.
827. Lowpass Butterworth filter of order n :  The flattest low-frequency response.
828. Linkwitz-Riley crossover filters  are used in modern active audio crossovers.
829. Chebyshev filters:  Ripples in either the passband or the stopband.
830. Elliptic (Cauer) filters  encompass all Butterworth and Chebyshev types.
831. Legendre filters  maximal roll-off rate with a monotonous frequency response.
832. Gegenbauer filters:  From Butterworth to Chebyshev, via Legendre.
833. Phase response  of a filter.
834. Bessel-Thomson filters:  Phase linearity and group delay.
835. Gaussian filters:  Focusing on time-domain communication pulses.
836. Linear Phase Equiripple:  Ripples in group delay to improve on Bessel filters.
837. DSL filter  allows POTS below 3400 Hz and blocks digital data above 25 kHz.

     Fantasy Engineering: Just for fun.

838. Raising the Titanic, with (a lot of) hydrogen.
839. Gravitational Subway:  From here to anywhere in 42 minutes.
840. In a vacuum tube, a drop to the center of the Earth would take 21 minutes.

     Steam Engines

841. The aeolipile:  This ancient steam engine demonstrates jet propulsion.
842. Edward Somerset of Worcester (1601-1667):  Blueprint for a steam fountain.
843. Denis Papin (1647-1714):  Pressure cooking and the first piston engine.
844. Thomas Savery (c.1650-1715):  Two pistons and an independent boiler.
845. Thomas Newcomen (1663-1729) and John Calley:  Atmospheric steam engine.
846. Nicolas-Joseph Cugnot (1725-1804):  The first automobile  (October 1769).
847. James Watt (1736-1819):  Steam condenser and  Watt governor.
848. Richard Trevithick (1771-1833) and the first railroad locomotives.
849. Sadi Carnot (1796-1832):  Carnot's cycle and the theoretical  efficiency limit.
850. Sir Charles Parsons (1854-1931):  The modern steam  turbine, born in 1884.

     Thermodynamics

851. The elementary concept of temperature.  The zeroth law of thermodynamics.
852. Conservation of energy:  The first law of thermodynamics.
853. Increase of Entropy:  The second law of thermodynamics.
854. State variables:  Extensive  and  intensive  quantities.
855. Entropy  is  missing information, a measure of  disorder.
856. Nernst Principle  (third law):  Entropy is zero at zero temperature.
857. Thermodynamic potentials  can be convenient alternatives to  internal energy.
858. Latent heat  (L)  is the heat transferred in a change of  phase.
859. Calorimetric coefficients, adiabatic coefficient  (g)  heat capacities, etc.
860. Cryogenic coefficients:  Lower temperature with an  isenthalpic  expansion.
861. Relativistic considerations:  A moving body appears  cooler.
862. Inertia of energy  for an object at nonzero temperature.
863. Stefan's Law:  A black body radiates as the fourth power of its temperature.
864. The "Fourth Law":  Is there really an upper bound to temperature?
865. Hawking radiation:  On the entropy and temperature of a black hole.
866. Partition function:  The cornerstone of the statistical approach.

     Demons of Classical Physics

867. Laplace's Demon:  Deducing past and future from a detailed snapshot.
868. Maxwell's Demon:  Trading information for entropy.
869. Shockley's Ideal Diode Equation:  Diodes don't violate the Second Law.
870. Szilard's engine & Landauer's Principle: The thermodynamic cost of  forgetting.

     Statistical Physics

871. Lagrange multipliers  are associated to the constraints of a maximizing problem.
872. Microcanonical equilibrium:  All states of an isolated system are equiprobable.
873. Canonical equilibrium:  In a heat bath, probabilities involve a Boltzmann factor.
874. Grand-canonical equilibrium  when  chemical  exchanges are possible.
875. Bose-Einstein statistics:  One state may be occupied by  many  particles.
876. Fermi-Dirac statistics:  One state is occupied by  at most one  particle.
877. Boltzmann statistics:  The  low-occupancy limit  (most states are unoccupied).
878. Maxwell-Boltzmann distribution  of molecular speeds in an  ideal gas.
879. Partition function:  The cornerstone of the statistical approach.

     Quantum Mechanics

880. Quantum Logic:  The surprising way quantum probabilities are obtained.
881. Swapping particles  either  negates the quantum state  or  leaves it unchanged.
882. The Measurement Dilemma:  What makes  Schrödinger's cat  so special?
883. Matrix Mechanics:  Neither measurements nor matrices can be switched at will.
884. Schrödinger's Equation:  A nonrelativistic quantum particle in a classical field.
885. Noether's Theorem:  Conservation laws express the symmetries of physics.
886. Kets  are Hilbert vectors (their duals are bras) on which observables operate.
887. Observables  are operators explicitely associated with physical quantities.
888. Commutators are the quantities which determine  uncertainty relations.
889. Uncertainty relations  hold whenever the commutator does not vanish.
890. Spin  is a form of angular momentum without a classical equivalent.
891. Pauli matrices:  Three 2 by 2 matrices with  eigenvalues  +1 and -1.
892. Quantum Entanglement:  The  singlet  and  triplet  states of two electrons.
893. Bell's inequality  is violated for the  singlet  state of two electron spins.
894. Generalizations of Pauli matrices  beyond spin ½.
895. Density operators  are quantum representations of imperfectly known states.

     Quantum Field Theory

896. Elementary particles:  Quarks and leptons.  Electroweak bosons.  Graviton?
897. Second Quantization:  Particles are modes of a quantized field.
898. Bethe-Salpeter Equation:  A relativistic equation for bound-state problems.

     Ancient Recipes and Modern Chemistry

899. Black Powder:  An ancient explosive, still used as a propellant (gunpowder).
900. Predicting explosive reactions:  A useful but oversimplified rule of thumb.
901. Thermite  generates temperatures hot enough to weld iron.
902. Enthalpy of Formation:  The tabulated data which gives energy balances.
903. Gibbs Function  (free energy):  Its sign indicates the direction of spontaneity.
904. Labile  is not quite the same as  unstable.
905. Inks:  India ink, atramentum, cinnabar (Chinese red HgS), iron gall ink, etc.
906. Beeswax  is dominated by a long-chain ester  (i.e., a "wax")  called  mycerin.
907. Pine pitch & cedar pitch:  Two similar products with different properties.
908. Gum Arabic:  The  magic bullet  of ancient chemistry.
909. Redox Reactions:  Oxidizers are reduced by accepting electrons...
910. Gold Chemistry:  Aqua regia ("Royal Water") dissolves gold and platinum.
911. Who was the "father" of modern chemistry?
912. Birth of organic chemistry:  Urea  was first synthesized  chemically  in 1828.
913. Aliphatic saturated hydrocarbons  are called  alkanes.
914. Unsaturated hydrocarbons  feature some carbon atoms tied by multiple bonds.
915. Functional groups  determine the basic reactions of  organic chemistry.

     Medicine by the Numbers

916. International Unit  (IU) is an arbitrarily-defined rating of  biological activity.
917. Concentration  is an amount (either mass or moles) per volume.
918. Glycosylated hemoglobin  (HbA1c) relates to  average  blood glucose (bG).

     Cosmology 101

919. Kant's Island Universes:  The Universe is filled with  separate  galaxies.
920. The Cosmological Principle: The Universe is homogeneous and isotropic.
921. The Big Bang:  An idea of Georges Lemaître  mocked by Fred Hoyle.
922. The Cosmic Microwave Background (CMB): Its spectrum and density.
923. Cosmic redshift (z):  Light emitted in a Universe which was (1+z) times smaller.
924. Hubble Law:  The relation between redshift and distance for comoving points.
925. Omega (W): The ratio of the density of the Universe to the critical density.
926. Look-Back Time:  The time ellapsed since observed light was emitted.
927. Distance:  In a cosmological context, there are several flavors to the concept.
928. Comoving points are reference points following the expansion of the universe.
929. The Anthropic Principle: An obvious explanation which may not be the final one.
930. Dark matter & dark energy: Gravity betrays the existence of some  dark  stuff.
931. The Pioneer Effect: The anomalous escape of the Pioneer spaceprobe.

     Stars and Stellar Objects

932. Nuclear fusion  is what powers the stars.
933. Brown dwarves  fail to ignite fusion.  They glow from gravitational contraction.
934. The Jeans mass  above which a gas at temperature T collapses gravitationally.
935. Main sequence:  The evolution of a typical star.
936. Eta Carinae  and  hypergiants.  The most massive stars possible.
937. Betelgeuse  and red supergiants.
938. Rigel  and blue supergiants.
939. Planetary nebulae:  Aftermaths of stellar explosions.
940. White dwarfs:  The ultimate fate of our Sun and other small stars.
941. Neutron stars:  Remnants from the supernova collapse of medium-sized stars.
942. Stellar black holes:  They form when supermassive stars run out of nuclear fuel.
943. Stellar X-ray source:  A small  accretor  in tight orbit around a  donor  star.

     The Solar System

944. Astronomical unit:  The precise definition of a standard unit of length.
945. The solar corona  is a very hot region of rarefied gas.
946. Solar radiation:  The Sun has radiated away about 0.03% of its mass.
947. The Titius-Bode Law: A numerical pattern in solar orbits?
948. The 4 inner rocky planets:  Mercury, Venus, Earth, Mars.
949. Earth:  This  is home.
950. The asteroid belt:  Planetoids and bolids between Mars and Jupiter.
951. The 4 giant gaseous planets: Jupiter, Saturn, Uranus, Neptune.
952. The discovery of Neptune:  Urbain Le Verrier  scooped John Couch Adams.
953. Pluto  and other  Kuiper Belt Objects  (KBO).
954. Sedna  and other planetoids beyond the  Kuiper Belt.
955. What's a planet?  Anything besides the 6 ancient planets, Uranus & Neptune?
956. Heliosphere and Heliopause:  The domain where solar wind exerts its influence.
957. Oort's Cloud  is a cometary reservoir at the fringe of the Solar System.

     Practical Formulas

958. Easy conversion between Fahrenheit and Celsius scales:  F+40  =  1.8 (C+40).
     Automotive :
959. Car speed is proportional to tire diameter and engine rpm, divided by gear ratio.
960. Car acceleration. Guessing the curve from standard data.
961. "0 to 60 mph" time, obtained from vehicle mass and actual average power.
962. Thrust  is the power to speed ratio (measuring speed along thrust direction).
963. Power of an engine as a function of its size:  Rating internal combustion engines.
964. Optimal gear ratio  to maximize top speed on a flat road  (no wind).
     Surface Areas :
965. Heron's Formula (for the area of a triangle) is related to the Law of Cosines.
966. Brahmagupta's Formula gives the area of a quadrilateral  (cyclic  or not).
967. Bretschneider's Formula: Area of a quadrilateral of known sides and diagonals.
968. The (vector) area of a quadrilateral  is  half  the cross-product of its diagonals.
969. Parabolic segment:  2/3 the area of a circumscribed parallelogram or triangle.
     Volumes :
970. Content of a cylindrical tank (horizontal axis), given the height of the liquid in it.
971. Volume of a spherical cap, or content of an elliptical vessel, given liquid height.
972. Content of a cistern (cylindrical with elliptical ends), as a function of fluid height.
973. Volume of a cylinder or prism, possibly with tilted [nonparallel] bases.
974. Volume of a conical frustum:  Formerly a staple of elementary education...
975. Volume of a sphere...  obtained by subtracting a cone from a cylinder !
976. The volume of a tetrahedron  is the determinant of three edges, divided by 6.
977. Volume of a wedge of a cone.
     Averages :
978. Splitting a job evenly between two unlike workers.
979. Splitting a job unevenly between two unlike workers.
980. Alcohol solutions are rated by volume not by mass.
981. Mixing solutions to obtain a predetermined intermediate rating.
982. Special averages: harmonic (for speeds), geometric (for rates), etc.
983. Mean Gregorian month: either 30.436875 days, or 30.458729474253406983...
984. The arithmetic-geometric mean  is related to a  complete elliptic integral.
     Geodesy and Astronomy :
985. Distance to ocean horizon line is proportional to the square root of your altitude.
986. Distance between two points on a great circle at the surface of the Earth.
987. Euclidean distance between two cities, along a straight line  through  the Earth.
988. The figure of the Earth. Geodetic and geocentric latitudes.
989. Kepler's Third Law: The relation between orbital period and orbit size.
      

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     Perimeter of an Ellipse

990. Circumference of an ellipse: Introducing exact series and approximate formulas.
991. Ramanujan I and Lindner formulas:  The journey begins...
992. Ramanujan II:  An awesome approximation from a mathematical genius (1914).
993. Hudson's Formula and other  Padé approximations.
994. Peano's Formula:  The sum of two approximations with cancelling errors.
995. The YNOT formula  (Maertens, 2000.  Tasdelen, 1959).
996. Euler's formula is the first step in an exact expansion.
997. Naive formula:  p  ( a + b )  features a  -21.5% error for elongated ellipses.
998. Cantrell's Formula:  A modern attempt with an overall accuracy of 83 ppm.
999. From Kepler to Muir.  Lower bounds and other approximations.
1000. Relative error cancellations in symmetrical approximative formulas.
1001. Complementary convergences of two series yield a nice foolproof algorithm.
       
1002. Padé approximants  are used in a whole family of approximations...
1003. Improving Ramanujan II  over the whole range of eccentricities.
1004. The Arctangent Function as a component of several approximate formulas.
1005. Abed's formula uses a parametric exponent to fine-tune the approximation.
1006. Zafary's formula.
1007. Rivera's formula gives the perimeter of an ellipse with 104 ppm accuracy.
1008. Better accuracy from Cantrell, building on his own previous formula
1009. Rediscovering  a well-known exact expansion due to Euler (1773).
1010. Exact expressions for the circumference of an ellipse:  A summary.

      Surface Area of an Ellipsoid

1011. Surface Area of a Scalene Ellipsoid:  The general formula isn't elementary.
1012. Thomsen's Formula:  A simple symmetrical approximation.
1013. Approximate formulas  for the surface area of a scalene ellipsoid.
1014. Nautical mile:  "Average"  minute of latitude  on an oblate spheroid.

      The Unexplained

1015. The Magnetic Field of the Earth.
1016. Life (1):  The mysteries of evolution.
1017. Life (2):  The origins of life on Earth.
1018. Life (3):  Does extraterrestrial life exist?  Is there intelligence out there?
1019. Nemesis: A distant companion to the Sun could explain extinction periodicity.
1020. Current Challenges to established dogma.
1021. Unexplained artifacts and sightings.

      Open Questions (or tough answers)

1022. The Riemann Hypothesis:   {Re(z) > 0   &   z(z) = 0}   Þ   {Re(z) = ½}.
1023. P = NP ?   Can we  find  in polynomial time whatever we can  check  that fast?
1024. Collatz sequences go from n to n/2 (iff n is even) or 3n+1. Do they all lead to 1?
1025. The Poincaré Conjecture  was proven by  Grisha Perelman  in 2002.

      Mathematical Miracles

1026. The only magic hexagon.
1027. The law of small numbers applied to conversion factors.
1028. Quadratic formulas yielding long sequences of prime numbers.
1029. The area under a Gaussian curve  involves the square root of  p
1030. Exceptional simple Lie groups.
1031. Monstrous Moonshine in Number Theory.

      Trivia

1032. Oldest unsolved mathematical problem:  Are there any odd perfect numbers?
1033. Magnetic Field of the Earth: The south side is near the geographic north pole.
1034. From the north side,  a counterclockwise angle is positive  by definition.
1035. What initiates the wind?  Well, primitive answers were not so wrong...
1036. Why "m" for the slope of a linear function  y = m x + b ? [English textbooks]
1037. The diamond mark on US tape measures corresponds to 8/5 of a foot.
1038. Naming the largest possible number, in n keystrokes or less (Excel syntax).
1039. The "odds in favor" of poker hands: A popular way to express probabilities.
1040. Reverse number sequence(s) on the verso of a book's title page.
1041. Living species: About 1400 000 have been named, but there are many more.
1042. Dimes and pennies: The masses of all current US coins.
1043. Pound of pennies: The dollar equivalent of a pound of pennies is increasing!
1044. Nickels per gallon: Packing as much as 5252.5523 coins per gallon of space.

      Geography, Geographical Trivia

1045. The volume of the Grand Canyon  would be 2 cm (3/4") over the entire Earth.
1046. The Oldest City in the World: Damascus or Jericho?
1047. USA (States & Territories): Postal and area codes, capitals, statehoods, etc.

      Handheld Calculators:  TI-92, TI-92+, TI-89, Voyage 200

1048. Keyboard and modifier keys.  Lesser-used functions require several keystrokes.
1049. Physical units:  A very nice afterthought, with some unfortunate rough edges.
1050. Real analytical functions  may present discontinuity  cliffs  in the complex realm.
1051. 68000 Assembly Programming:  A primer without the help of an assembler.
1052. The clock frequency of your calculator:  How to measure it with 0.1% accuracy.
1053. BASIC Programming.  TI's built-in interpreted language is convenient but slow.

      Money, Currency, Precious Metals

1054. Inventing Money: Brass in China, electrum in Lydia, gold and silver staters...
1055. Prices of Precious Metals:  Current market values (Gold, Silver. Pt, Pd, Rh).
1056. Medieval sysyem:  12  deniers  to a  sol.
1057. Ancien Régime  French monetary system.
1058. British coinage  before decimalization.
1059. Exchange rates  when the  euro  was born.
1060. Worldwide circulation  of currencies.

      The Counterfeit Penny Problem

1061. Counterfeit Coin Problem: In 3 weighings, find an odd object among 12, 13, 14.
1062. General Counterfeit Penny Problem: Find an odd object in the fewest weighings.
1063. Explicit tables  for detecting  one  odd marble among  41,  in  4  weighings.
1064. Find-a-birthday:  Detect an odd marble among 365, in 6 weighings.
1065. Error-correcting codes for ternary numeration.
1066. If the counterfeit is known to be heavier, fewer weighings may be sufficient.

      Calendars & Chronology

1067. Fossil calendars: 420 million years ago, a lunar month was only 9 short days.
1068. Julian Day Number (JDN) Counting days in the simplest of all calendars.
1069. The Week has not always been a period of seven days.
1070. Egyptian year of 365 days: Back to the same season after over 1500 years.
1071. Heliacal rising of Sirius: Sothic dating.
1072. Coptic Calendar: Reformed Egyptian calendar based on the Julian year.
1073. The Julian Calendar: Year starts March 25. Every fourth year is a leap year.
1074. Anno Domini: Counting roughly from the birth of Jesus Christ.
1075. The Gregorian Calendar: Multiples of 100 not divisible by 400 aren't leap years.
1076. Counting the days between dates, with a simple formula for month numbers.
1077. Age of the Moon, based on a mean synodic month of  29.530588853 days.
1078. Easter Sunday is defined as the first Sunday after the Paschal full moon.
1079. The Muslim Calendar:  The Islamic (Hijri) Calendar (AH = Anno Hegirae).
1080. The Jewish Calendar:  An accurate lunisolar calendar, set down by Hillel II.
1081. Zoroastrian Calendar.
1082. The Zodiac:  Zodiacal signs and constellations.  Precession of equinoxes.
1083. The Iranian Calendar.  Solar Hejri [SH]  or  Anno Persarum  [AP].
1084. The Chinese Calendar.
1085. The Japanese Calendar.
1086. Mayan System(s):  Haab (365), Tzolkin (260), Round (18980), Long Count.
1087. Indian Calendar:  The Sun goes through a zodiacal sign in a solar month.
1088. Post-Gregorian Calendars:  Painless  improvements to the secular calendar.
1089. Geologic Time Scale:  Beyond all calendars.

      Roman Numerals  (Archaic, Classic and Medieval)

1090. Roman Numeration: The basics and the precise rules (including medieval ones).
1091. Larger Numbers, like 18034...
1092. Extending the Roman system.
1093. IIS (or HS) is for sesterce (originally, 2½ asses, "unus et unus et semis").

      Humor

1094. Standard jokes.
1095. Limericks.
1096. Proper credit may not always be possible.
1097. Trick questions can be legitimate ones.
1098. Ignorance is bliss:  Why not read all that mathematical stuff  faster ?
1099. Silly answers to funny questions.
1100. Why did the chicken cross the road?  Scientific and other explanations.
1101. Humorous or inspirational quotations by famous scientists and others.
1102. Famous Last Words:  Proofs that the guesses of experts are just guesses.
1103. Famous anecdotes.
1104. Parodies, hoaxes, and practical jokes.
1105. Omnia vulnerant, ultima necat:  The day of reckoning.
1106. Funny Units: A millihelen is the amount of beauty that launches one ship.
1107. Funny Prefixes: A lottagram is many grams; an electron weighs 0.91 lottogram.
1108. The Lamppost Theory:  Look only where there's enough light to find anything.
1109. Anagrams: Rearranging letters may reveal hidden meanings ;-)
1110. Mnemonics: Remembering things and/or making fun of them.
1111. Acronyms: Funny ones and/or alternate interpretations of serious ones.
1112. Usenet Acronyms: If you can't beat them, join them (and HF, LOL).

      Scientific Symbols and Icons

1113. The equality symbol ( = ).  The "equal sign" dates back to the 16th century.
1114. "Lines" among symbols: Vinculum, bar, solidus, virgule, slash, macron, etc.
1115. The infinity symbol ( ¥ ) introduced in 1655 by John Wallis (1616-1703).
1116. Transfinite numbers:  Mathematical symbols for the multiple faces of infinity.
1117. Chrevron symbols:  Intersection (highest below)  or  union (lowest above).
1118. Disjoint union.  Square "U" or  inverted  p  symbol.
1119. Blackboard bold:  Doublestruck  symbols are often used for sets of numbers.
1120. The integration sign ( ò ) introduced by Leibniz at the dawn of Calculus.
1121. The end-of-proof box (or tombstone) is called a halmos symbol  (QED).
1122. Two "del" symbols:  ¶  for partial derivatives, and  Ñ  for Hamilton's nabla.
1123. The Staff of Aesculapius:  Medicine and the 13th zodiacal constellation.
1124. The Caduceus:  Scepter of Hermes, symbol of  commerce  (not medicine).
1125. The Tetractys: Mystical Pythagorean symbol, "source of everflowing Nature".
1126. The Borromean Rings: Three interwoven rings which are pairwise separate.
1127. The Tai-Chi Mandala: The taiji (Yin-Yang) symbol was Bohr's coat-of-arms.

      Unabridged Answers (monographs and complements):

1128. Sagan's number:  The number of stars, compared to earthly grains of sand.
1129. The Sand Reckoner:  Archimedes fills the cosmos with grains of sand.
       
1130. About Zero.
1131. Wilson's Theorem.
1132. Counting Polyhedra:  A tally of polyhedra with n faces and k edges.

      Hall of Fame:

1133. Numericana's list of distinguished Web authors in Science...  Links to their sites.
1134. Giants of Science:  Towering characters in the history of Science.
1135. Two legendary Solvay conferences  defined modern physics, in 1911 and 1927.
1136. Physical Units: A tribute to the late physicist Richard P. Feynman (Nobel 1965).
1137. The many faces of Nicolas Bourbaki  (b. January 14, 1935).
1138. Lucien Refleu  (1920-2005).  "Papa" of 600 mathematicians.  [ In French ]
1139. Roger Apéry  (1916-1994)  and the irrationality of  z(3).
1140. Hergé (1907-1983):  Tintin and the Science of Jules Verne (1828-1905).
1141. Escutcheons of Science (Armorial):  Coats-of-arms of illustrious scientists.
      • Supplementary Armorial:  Contemporary scientists, engineers, explorers...

Noted   Numericana Fans  (and/or contributors)  in alphabetical order:

• Max Alekseyev,  Silent Circles.
• David Cantrell,  Perimeter of an Ellipse  (2001, 2004, etc.)
• Joe Crump,  Carmichael Divisors.
• Paul Godfrey,  Lanczos Formula.
• Michel Marcus,  Hemiperfect Numbers  (11/2, 13/2, 15/2).
• Belisha Price,  Polyhedra.
• Knud Thomsen,  Surface Area of an Ellipsoid.
• Robin Whitty,  Theorems.
• Jochen Wilke,  Escutcheons of Science.

Guest Authors:

• Lanczos Implementation of the Gamma Function   by Paul Godfrey.

Public-Domain Texts:

• Preliminary report (1819) on the British Weights and Measures reform of 1824.

Some Recent Reciprocal Links
(Pages quoting Numericana's "Final Answers")
2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001

• Infinity Symbol  by  HS student  Christina Hernandez   (before 2010-02-05).
• Perimeter of an ellipse  (in Russian)  by  mkay422   (2010-02-04).
• Integration symbol  by  Okay   (2010-02-04).
• Lewis Carroll's Monkey Puzzle  by  Bigtop   (2010-02-04).
• Math is Math...  by  Tom Nalevanko   (2010-02-03).
• The Five-Card Trick  of  Fitch Cheney  by  David Speyer   (2010-02-02).
• Escutcheons of Science  by  Peter Meister   (2010-02-01).
• Arms of Galileo  by  Bernhard Peter = Herold-vom-Rhein   (2010-01-28).
• Euler-Descartes equation  by  19106   (2010-01-21).
• 10 Great Sites for Geeking Out  by  Pi Guy   (2010-01-17).
• Distance from Alexandria to Aswan:  What's 5000 stadia?   (bef. 2010-01-17).
• Rediscovering an ancient glue  [ 2 ]   by  Jerome A. Samounce  (2010-01-11).
• The amazing mouth of Kreskin  and  Math Magic  (2010-01-03).
• Magic The Gathering: A to Z.  Artificial Gibberish   (2009-12-29).
• Magic The Gathering: A to Z.  Arcane gibberish   (2009-12-29).
• Obsolete inches (USMA)  by  John Steele  &  Pat Naughtin  (2009-12-28).
• Black diamonds on a tape measure   by  Woodeneye   (2009-12-22).
• The polyominoes of Sol Golomb   by  Travis Hale  (2009-12-15).
• ¿ Por qué no es primo el  1 ?  FAQ  at  MaTeTam  (before 2009-12-12).
• Thomsen's formula  by  Cavarretta, O'Sullivan & Coop  (bef. 2009-12-08).
• Ternary Magic Cards  at  Oakland/East Bay Math Circle  (bef. 2009-12-08).
• Inclusion-Exclusion  (with short URL)  by  Jordan Cole  (2009-12-06).
• Thomsen's formula  by  Richard F. Burton  (2009-12-01).
• Blason de François Viète (in French)  by  Jean de Parthenay  (2009-11-25).
• Symbol for the set of prime numbers  by  APcalculus  (2009-11-24).
• Circumference of an Ellipse  by  David Biddulph  (2009-11-24).
• On the Perimeter of an Ellipse  by  Paul Abbott  (before 2009-11-23).
• Cycling Performance Simplified  by  Bob Fugett  (2009-11-22).
• Legendre who?   (Division by Zero)  by  Dave Richeson  (2009-11-19).
• The scary face of a great mathematician  in Korean   (2009-11-17)
• Legendre != Legendre   Programa de Educação Tutorial  (2009-11-16)
• Wow... I must buy this book!!!  by  Peter Theoh   (2009-11-16)
• Pythagoras Constant  at  Barcodes, Inc.   (before 2009-11-16)
• The Orbode Company  links by  Angelo   (before 2009-11-16)
• Theoretische Elektrotechnik   by  Karl Küpfmüller  (before 2009-11-16)
• Legendre, we hardly knew ye!   in  Ars Mathematica  (2009-11-15)
• Legendre on Wikimedia Commons  thanks to  Pieter Kuiper  (2009-11-14)
• Mistaken portrait of Legendre (Notices AMS)  by  Peter Duren  (2009-11-11).
• Gray Elephants in Denmark  by  Buckwheat469   (2009-11-10).
• About Abundancy  by  Walter Nissen  & Michel Marcus   (bef. 2009-11-08).
• Superabundant numbers, etc. (in French)  by  mam   (2009-11-06).
• Scientific biographies  by  Robin Whitty   (bef. 2009-11-02).
• Polyhedra by Belisha Price, retired legend of Cambridge HS  (bef. 2009-10-27).
• Stars in Galaxy, galaxies in Universe  at  Ecolution Trail   (bef. 2009-10-24).
• Coat-of-arms of printers (in Finnish)  by  Eero Hämäläinen  (bef. 2009-10-23).
• Tycho Brahe  (in A Universe in Time)  by  Ken R. Pinkela   (bef. 2009-10-21).
• BENG 221  Math. Methods in Bioengineering,  at UCSD  (bef. 2009-10-19).
• Crazy about numbers  by  himanshupratap   (2009-10-18).
• Portrait of Legendre  (in Russian)  by  iv6   (2009-10-17).
• Bohr's coat-of-arms  (in Dutch)  by  Michelin   (2009-10-11).
• Arms of Leonardo da Vinci (in Catalan)  by  JM   (2009-10-08).
• Mathematics Help  by  Dr. Bruce W. Coletti   (before 2009-10-04).
• What is the circumference of an ellipse?   WikiAnswers   (before 2009-10-03).
• How to simulate a Poisson process  by  Harry Kim   (2009-09-30).
• Legendre & Fourier caricatures  by  Stpasha & Infofiltrage   (2009-09-29).
• Broken calculator with 6 keys   in Chinese   (before 2009-09-28).
• SAM 206 - Septenber 2009  by  Opie Houston   (before 2009-09-22).
• Knight & Day  (Niels Bohr)  by  Elizabeth Reninger   (2009-09-23).
• Lewis Carrol's Monkey Puzzle  in Japanese   (2009-09-17).
• The Magic of 9  by  Pi Guy   (2009-09-10).
• Mathematics Help on the Internet   in Finnish   (before 2009-09-09).
• Erroneous portrait of Legendre  Wikipedia deletion request   (2009-09-07).
• Multiplication of complex numbers  by  David   (2009-09-04).
• Nautical Leagues  by  Valentine   (2009-09-01).
• First Solvay Conference (1911)  in  CosmoLearning   (bef. 2009-08-31).
• Arms of August Wilhelm von Hofmann  by  Jochen Wilke   (2009-08-29).
• Militant blogs  (in Czech)  by  Satori   (2009-08-27).
• Kevin S. Brown & MathPages  (in Polish)  by  5-Grid   (2009-08-14).
• Coat-of-arms of Werhner v. Braun  (in German)  by  Björnson  (2009-08-12).
• Mathematik  (in German)  by  Frank Dreßler   (2009-08-06).
• Numericana's hall of fame  (in Swedish)  by  Tonyf   (2009-08-03).
• Perimeter of an ellipse,  in Japanese  (2009-08-01).
• M. Pfeifer = Le Bicou  Taupe Ampère, Lycée Thiers  (bef. 2009-07-31).
• Along Came Leonhard Euler  by  HumblyTheirs  (2009-07-30).
• Ramanujan's number  by  Graham D  (2009-07-30).
• Sum of the reciprocals of Catalan numbers  by  Juan Márquez  (2009-07-29).
• About Numericana  (in Russian) ... and the  Symbol font  (2009-07-26).
• Coats-of-Arms of Nobel Laureates  by  Jochen Wilke  (2009-07-14).
• Tetragonal Antiprism  (in German)  by  Jürgen Köller  (before 2009-07-01).
• Graduation speech  commented by  Jonathan Vos Post   (2009-06-29).
• On multiple-choice questions  in  Terry Tao's blog   (2009-06-29).
• 50th birthday of Glénisson's formulas  (in French)  by  Doris   (2009-06-28).
• Zillions  by  JimmyG  at AnswerBag.com   (2009-06-27).
• 24 Tintin albums  by  @Li3n   (2009-06-26).
• Wythoff's game on the quarter-plane  by  Aleph_One   (2009-06-24).
• Math Magic  by  Mrs. Schlueck, Hillside Grade School  (bef. 2009-06-23).
• Who wrote Reflections on Relativity ?  by  Blackhead   (2009-06-15).
• Diodes obey second law of thermodynamics  by  mrflora   (2009-06-14).
• Quadratic Reciprocity  by  Graeme McRae  (before 2009-06-09).
• Ellipsoid  (in German)  by  Jürgen Köller  (before 2009-06-08).
• Flattening a sphere  by  Yotch  (2009-06-07).
• Juan Pablo Muñoz's Library  at  diigo.com   (2009-06-04).
• Planar Curves  in  "Community College Calculus"  by Vlorbik  (2009-05-11).
• Was Leonardo da Vinci Catalan? (in Catalan)  by Jordi Bilbeny  (2009-05-11).
• Arms of Johan Gadolin (1760-1852)  by  Jochen Wilke  (2009-05-08).
• Arms of Pierre Deligne (b. 1944)  by  Jochen Wilke  (2009-05-07).
• Voyage 200 bookmarks  by  carlosvicunav  (before 2009-05-06).
• About Edouard Herzen  at  Lexilogia  by  Stathis  (2009-05-06).
• Continued Fractions  (book review)  by  A. Ya. Khinchin  (bef. 2009-05-06).
• Icosahedral die  ("scattergories cube")  by  Skateandscoot  (2009-05-02).
• Look-back time  by  Dave Mitsky  (2009-05-01).
• Pierre Deligne's coat-of-arms  [ 1 ]  by  Jordan S. Ellenberg  (2009-04-29).
• Circumference of an Ellipse  by  Shahram Zafary   (2009-04-21).
• Enumeration of polyhedra  (in German)  by  PhotonX   (2009-04-17).
• Ellipsoid  by  Shneider, Mentis, Schustak, and O'Donovan   (2009-04-15).
• The Kruskal Principle  by  Scott Cram   (2009-04-09).
• History of Logarithms  by  Ms. Fleming   (before 2009-04-05).
• Heraldry Links  by  Marek Nienaltowski   (before 2009-04-05).
• Perimeter of an Ellipse  (in Dutch)  by  Kjell   (2009-04-04).
• The constants of Mathematics  by  Chuck Knepfle   (before 2009-04-02).
• Numericana, Enciclopedia dei Numeri  by  Lorenzo Zaninetti   (2009-03-30).
• La aritmética p-ádica (in Spanish)  by  Remolon   (2009-03-27).
• Malo Mori Quam Foedari  by  Linda_J   (2009-03-09).
• Coat-of-arms of Hans Christian Ørsted  by  Jochen Wilke   (2009-02-21).
• Gear Design and Rack Radius  by  BabyBear   (2009-02-19).
• Feynman Apologetics  by  Viren Fernandes   (before 2009-02-15).
• Arms of Scientists and Explorers  by  Jochen Wilke   (2009-02-14).
• Coat-of-arms of Niels Bohr  (in Czech)  by  Faleristika   (2009-02-14).
• The 1089 force  by  fkace63   (2009-02-14).
• Introducing Numericana  at  www.hazemsakeek.com   (2009-02-09).
• Advice about ellipse formula  by  Noone   (2009-02-06).
• NationMaster > Encyclopedia > Benjamin Thompson   (before 2009-02-05).
• Units of Energy & Power  at  Instituto Superior Técnico   (2009-02-04).
• Brain Teasers  at  The Crafty Puzzles Company   (2009-02-03).
• Good On-Line Armorials  by  David B. Appleton   (before 2009-02-03).
• Doplnky o grupach  (in Slovakian)  by  Tomas Richta   (bef. 2009-01-29).
• Podrobneji o pologrupach  by  Tomas Richta   (before 2009-01-29).
• Demon of Laplace  in  The PC Engine Software Bible   (bef. 2009-01-26).
• Tycho Brahe and Hamlet  by  MinnesotaStan   (2009-01-24).
• The color of Tintin's hair  by  SheSaidDestroy   (2009-01-23).
• Coat-of-arms of Emperor Akihito  in  Out of Eden   (2009-01-21).
• Mathematical Symbols  by  Robin Whitty   (2009-01-20).
• Physics at Numericana  (in Japanese)  by  Shimota-79   (2009-01-17).
• Planck Length & Planck Time  (in German)  by  Ungläubige   (2009-01-17).
• Enumeration of Polyhedra  (in German)  by  PhotonX   (2009-01-17).
• Niels Bohr's coat-of-arms  (in German)  by  DrumDub   (2009-01-16).
• Differential Question  (Camaro automobile)  by  69 rs/ss   (2009-01-13).
• Dead Sea Scrolls and Iron Gall Ink  by  Count Iblis   (2009-01-12).
• Ideal Gases  by professor   Ruslan Ozerov   (before 2009-01-12).
• Balance Problem  by   Deepika   (2009-01-09).
• Perimeter of an ellipse  by  BadBoy   (2009-01-08).
• Languages in Images and Paintings  by  Imelda Almqvist   (2009-01-08).
• ADSL filters and Sky Digibox  by  Sam Radford   (before 2009-01-08).
• Scientific Symbols and Icons...  at  StumbleUpon   (before 2009-01-06).
• ADSL filters  by  Sam Radford   (2009-01-05).
• Kruskal Paths to God  by  Scott Cram   (2009-01-01).
• Tombstone Symbol  in WikiAnswers,  by  Hisoftsol   (before 2008-12-30).
• Last Year at Marienbad.  Numerical methods, in Polish   (bef. 2008-12-23).
• Introduction to Quantum Mechanics,  reviewed by  Dope-addict   (2008-12-22).
• 13th Zodiacal Symbol  (in Slovenian)   =   Staff of Aesculapius  (2008-12-18).
• A Little Physics Conundrum  by   Thoughtfully   (2008-12-15).
• Heraldic links  (in German)  at   GenWiki   (before 2008-12-13).
• Counterfeit coin problem  by   Vikas  (2008-12-07).
• Taoism and Bohr's Coat-of-Arms  by   NonTien  (2008-12-04).
• Einstein and Intellectual Property  by   Noah Callaway  (2008-12-02).
• Richard Feynman & Machine Needles  by  Quilting Kathy  (2008-11-29).
• Tons of fun math stuff  (Yahoo! Answers)  by  Josh S  (2008-11-25).
• Wanted Dead or Alive: Schrödinger's Cat  by  J  (2008-11-23).
• Bohr's coat-of-arms  in Estonian  (2008-11-20).
• Counting Abelian groups  by  NonCommAlg  (2008-11-16).
• Symbols, equality, yin-yang  on  Mrs. Carrigan's Math page  (bef. 2008-11-14).
• Coat-of-arms of Ferdinand von Zeppelin  by  Jochen Wilke  (2008-11-11).
• The Lamppost Theory  by  A.H. Roslan Harahap  (before 2008-11-08).
• Matemáticas y trucos mentales de cálculo  in Spanish   (2008-11-07).
• Academic Poker Resources  ay  Big Edge Poker  (before 2008-11-06).
• Introduction to Combinatorial Analysis  by  Levent Kandiller  (2008-11-03).
• Rosenkrantz and Guildenstern  coats-of-arms  by  Jerzi Lucki   (2008-10-31).
• Recommending the TI Voyager 200  (in Croatian)  by  Harry   (2008-10-30).
• Units of Measure [2]  Writing Resources  by  Alexander Burns  (2008-10-29).
• Lleonard Vinci  (in Catalan)  by  Joan Calsapeu  (2008-10-17).
• Solvay conferences  in links by  Lyzanor  at  delicious.com   (2008-10-10).
• Arms of Leonardo da Vinci  (in Catalan)  by  JM  (2008-10-08).
• Linear Systems  at  NCTM's Illuminations  (before 2008-10-08).
• Tropentag 2008  at the  University of Hohenheim   (2008-10-07).
• El escudo heráldico de Leonardo da Vinci  (in Catalan)  by  Pep  (2008-10-04).
• Arms of Leonardo da Vinci  (in Catalan)  by  Jordi Bilbeny  (2008-10-03).
• Maintaining a constant circumference  by  Bluechip   (2008-10-02).
• Fork in the road  by  Sanders  (2008-10-02).
• Tycho Brahe and William Shakespeare  by  Ian  (2008-09-29).
• Exact value of the horsepower  (hp)  by  Jay Belanger  (2008-09-25).
• Pullup assistant bands as ellipses  by  Cybercop  (2008-09-25).
• Daily Links  [ 1 ]  on  Webliminal  by  Ernest Ackermann  (2008-09-12).
• Comment calculer le périmètre d'une ellipse?   In French.   (2008-09-11).
• Rediscovering Mathematics  (MA 143)  by  Shai Simonson  (bef. 2008-09-11).
• Wernher von Braun  in Catalan [?]   (before 2008-08-16).
• Packing People in the Grand Canyon  by  Mikabee  (2008-08-15).
• Last Year at Marienbad  by  AngryCandy  (2008-08-09).
• Szilard's engine  (in Japanese)  by  hiroki_f   (2008-08-04).
• Parabolic arc length  by  11rdc11   (2008-08-03).
• Maxwell Equations & Lorentz Force  by  Zentara   (2008-08-01).
• The Symbol font problem  by  David W. Knight  (bef. 2008-07-31).
• Wythoff's Game,  M.A. thesis by  Kimberly Hirschfeld-Cotton  (July 2008).
• Kilotons & megatons.  United Nations Cyberschoolbus  (bef. 2008-07-30).
• Polyhedra with large number of edges  by Andreas Rüdinger   (2008-07-28).
• Apéry's Constant  by Shane   (2008-07-28).
• Ed Pegg, Jr.  (anagram)  by Rotund Filipino   (2008-07-24).
• Smallest recorded measurement  by  Brian  at  Answerbag   (2008-07-19).
• Fun Site  by  Trisha   (2008-07-13).
• Set Theory  at  GiftedResources.org   (before 2008-07-10).
• Thomsen's formulae  by  Kingston, Clayton, Priest and Best   (2008-07-06).
• Links on Wikipedia  by  Robin Whitty "Charleswallingford"   (2008-06-25).
• Quick Snippets  (Grey Matters)  by  Scott Cram   (2008-06-05).
• How many elephants are there in Denmark?  by  Ned Kelly   (2008-05-31).
• Visit to the 7-11  by  ChuckJerry   (2008-05-29).
• Mathematical Brooding over an Egg  by  André Heck   (before 2008-05-27).
• The diamond mark at every 19.2"  by  kpepin   (2008-05-21).
• Coriolis deviation in a  Tower of Pisa  drop  by  Markogts   (2008-05-21).
• Meaning of h-bar symbol  by  Starman   (2008-05-19).
• Number Theory Education Resources  by  Mike  at  mahalo.com  (2008-05-13).
• Escutcheons of Science  at  Forum-Rycerstwa   (before 2008-05-13).
• Billion  on  The Timber Yard  by  Noddy330   (2008-05-04).
• Périmètre d'une ellipse  (in French)  by  Valeri Astanoff   (2008-05-04).
• Escudos de Científicos  by  Jose Juan Carrion Rangel   (2008-04-27).
• Iron-gall ink in a fountain pen  by  Ondina   (2008-04-14).
• Funny units  by  bp56   (2008-04-13).
• Wilson's Theorem  by  Balan   (2008-04-09).
• Perimeter of an Ellipse  by  Hellburner  at ars technica   (2008-04-09).
• Numericana Hall of Fame  by  Seth Tyler  at ISH   (before 2008-04-01).
• Bohr's coat-of-arms  (in Latvian)  by  Ierindnieks   (2008-03-28).
• Naming Polyhedra  [ 1 | 2 ]  (in German)  by  Hugo Pfoertner   (2008-03-26).
• Demons of Physics  by  Ughaibu   (2008-03-23).
• Library Links  Metropolitan Community College,  MO   (bef. 2008-03-22).
• Steven Weinberg  by  Pentcho Valev   (2008-03-21).
• Feynman on Physical Units  by  Henry L. Neal  at CAU   (bef. 2008-03-18).
• Famous Scientists: Archimedes  by  Marie P.,  4th Grade  (2008-03-10).
• Quick witted student learns to deadpan  by  Gregg Chenoweth  (2008-02-25).
• C183 and C209  by  Rogue,  updated by  Fivemack   (2008-02-14).
• Wieferich-related factoring  (C183, C209)  [ 1 ]  by  Zeta-Flux   (2008-02-13).
• Circumference of an ellipse in QBasic and Lisp,  by  tcebob   (2008-02-11).
• The Natural Number  e  by  Stirling Stan   (2008-02-10).
• Perimeter of an ellipse  by  John Nimphius   (2008-02-03).
• Borromean rings  by  Emlaabs   (2008-01-30).
• Blason de Adrien-Marie Legendre  by  Infofiltrage   (2008-01-28).
• Mathematics  at  2000clicks.com   (2008-01-26).
• Multiplying Nimbers  by  Joshua Zucker   (2008-01-17).
• Hacks  (Funny Units)  by  Dr. Jeremy Frank  of NASA   (2008-01-15).
• Cool math-magic sites  by  John Dougherty   (before 2008-01-11).
• Math Symbol (Equal sign)  by  Lori Carrigan   (before 2008-01-11).
• Math Symbol (Equal sign)  by  Donette Carter   (before 2008-01-08).
• The elusive Kevin S. Brown  (in Russian)  by  Z.K. Silagadze   (2008-01-06).
• Archimedes Spiral  by  David McCombs.   (before 2008-01-03).
• Carmichael Multiples  by  Joe Crump.   (2008-01-02).
• The Tai-Chi or Yin-Yang symbol  by  Barbara   (2007-12-31).
• Pétrole, gaz et les autres énergies  by  Albert Legault   (bef. 2007-12-31).
• Surfing Note  in  Mathematics Teacher  by  Derek Smith   (bef. 2007-12-31).
• Abell 1835 IR1916  (in Spanish)  by  Horacio C.   (2007-12-30).
• Area of an Ellipsoid  (in French)  by  Cauchy   (2007-12-25).
• Length of an Ellipse  in Russian   (2007-12-24).
• Area of an Ellipsoid  (in French)  by  Zapple   (2007-12-23).
• Contraria Sunt Complementa  by  Kyle Matthew Oliver   (2007-12-17).
• Tycho Brahe  by  Lupo LeBoucher   (2007-12-10).
• Surface area of an elliptical dish head  by  Oil Field Trash   (2007-12-09).
• The experiment Galileo didn't do  by  Gideon Reich   (2007-12-01).
• Computing the partition function  (in Polish)  by  Samolot   (2007-11-25).
• About Millikan's experiments (in Polish)  by  Arkadiusz Jadczyk  (2007-11-24).
• Huge numbers in Roman nnumerals  by  Maryt/theteach   (2007-11-18).
• Arc length of a parabola  (University of Regina)  by  Harley   (bef. 2007-11-15).
• Fun with math?!  (true nature of magic)  by  Neutronjockey   (2007-11-14).
• From Slugs to Kegs  by  Snatirup   (2007-11-12).
• Grave of Count Rumford  by  John A. Robertson   (before 2007-11-11).
• Divisors of zero  (Math 651, Ohio State)  by  G.A. Edgar   (bef. 2007-11-08).
• Prominent Scientists.  Amman Baccalaureate School, Jordan  (2007-11-07).
• Epitaph of Roger Apéry  by  Bertrand Beyern   (before 2007-11-06).
• How many stars in the Andromeda galaxy  by  Chris Wagoner   (2007-11-04).
• Arms of Adrien-Marie Legendre  by  Infofiltrage   (2007-10-31).
• Squuzuu = Partition Function  by  Abbas   (2007-10-28).
• Circumference of an ellipse  by  Devrath   (2007-10-28).
• Historical Armorials  at  The Heraldry Society   (before 2007-10-27).
• Useful Stuff  by  J. Paul Gustafson  at Messiah College  (bef. 2007-10-25).
• Surface area of an ellipsoid  by  Raxit   (2007-10-24).
• Planar Curves  by  Bryan Bishop   (before 2007-10-24).
• Introduction to Group Theory  by  Anton Gorodetski  (before 2007-10-24).
• Sources / Fonti  for the  libconic  mathematical project   (before 2007-10-21).
• Credits / Meritii :  Perimeter of an ellipse for  libconic  (before 2007-10-21).
• DCMI Date Working Group  Dublin Core Metadata Initiative  (bef. 2007-10-21).
• 0^0 = 1  in  "The Student Room"  by  FusionSKD   (2007-10-20).
• Références mathématiques  [ 1 ]  by  MC  (before 2007-10-20).
• The Superfund Three-card Monte  by  TMFMarathonMan  (2007-10-19).
• Favorite Math Links  (in Finnish)  by  Janne Aukia  (2007-10-18).
• Favorite Links  (in Finnish)  by  Jannep  (2007-10-18).
• Miracle de la Monarchie  by  JesusFranco  on  zentropa.info  (2007-10-17).
• Best of the Web  about hexahedra, polyhedra & polytopes  (bef. 2007-10-17).
• Infinity  (patchwork of clippings)  Concord Middle School   (bef. 2007-10-14).
• Baltzar von Platen  by  Jeremy   (2007-10-11).
• Carmichael Zahlen  in  Meyers Lexikon   (before 2007-10-08).
• Taaffe Viscount  (in German)  by  Frank Martinoff   (2007-10-01).
• Two odd balls  (found by weighing with a balance)  by  Opalg   (2007-09-30).
• Arms of scientists  by  Stephen J.F. Plowman, TD FSA Scot  (2007-09-30).
• Volume of a Spheroid  by  LearnExcel  (2007-09-27).
• Mathematics & Physics [ 2 ] in Bulgarian, by B.B. Bantchev  (bef. 2007-09-26).
• Aurifeuillian Factorization   by  James Wanless   (2007-09-23).
• Stars vs. Sand Recounted  in  RASNZ newsletter, by  Laintal  (2007-09-23).
• Intégrales elliptiques de deuxième espèce  by  Framboise  (2007-09-22).
• Infinity symbol  for  Mrs. Martin's Fourth Grade  (before 2007-09-18).
• Fattest tetragonal antiwedge?  by  Erimo   (2007-09-17).
• Unit(s) for Planck's constant  (in German)  by Martin Müller   (2007-09-16).
• Tetragonal antiwedge  in  Erimo's Journal   (2007-09-15).
• A Mecânica do Século XVII  in  História da Ciência   (2007-09-04).
• Una vaschetta origami  by  Giorgio Vecchi   (2007-09-04).
• Really cool maths teasers  in  Orange Sunset   (2007-09-03).
• Prime Number  in  Conservapedia   (before 2007-09-01).
• 146 old pennies to a pound  by  Mitch Ross   (2007-08-29).
• Sir George Gabriel Stokes:  August 13 in Science History  (bef. 2007-08-28).
• Linki do ciekawych stron   Escutcheons of Science   (before 2007-08-22).
• Volume of the Grand Canyon  by  Orbinspace   (2007-08-21).
• EDC 5V95 Syllabus  by  Trena L. Wilkerson  at Baylor   (bef. 2007-08-20).
• Wernher von Braun  at  www.spock.com   (before 2007-08-20).
• Perimeter of an Ellipse  by  WesleySonofCornelius   (2007-08-16).
• Trigonometry Class  in  "The Classroom"   (before 2007-08-16).
• Useful Reference Web Sites  by  David G. Simpson  (before 2007-08-16).
• Another page Jim might like  by  Rybo  on GeoJourney   (2007-08-05).
• Michon's conjecture on Carmichael divisors  by  Maxal  (2007-08-05).
• Fundamentals of Electronics  by  Dr. Stephen McArthur  (bef. 2007-08-04).
• Good Websites  by  Forever May Not   (2007-08-01).
• Foundations of Mathematics  at  University of Brighton  (bef. 2007-07-31).
• Properties of Specific Numbers  by  Robert P. Munafo  (before 2007-07-31).
• Mathématiques ludiques  (in French)  by  Tropique  (2007-07-27).
• Another nice site  by  Galactus  at MathHelpForum   (2007-07-25).
• Arni's Mindgames  by  Chandru Arni   (before 2007-07-23).
• Wie das rad richtig benutzt wird  (in German)  by  Moriaan   (2007-07-21).
• Plankschen Konstante  (in German)  by  King_of_Loss   (2007-07-20).
• Comedy Shtick and Counterfeit Penny  by  D. Frisch   (2007-07-19).
• Grey Elephants in Denmark  by  Mark Runge   (2007-07-19).
• Niste rezolvari  (in Romanian)  by  Constantin Obreja   (2007-07-17).
• How to become a theoretical physicist  by  Bryan Bishop   (bef. 2007-07-16).
• German horsepower  by  Djmatty   (2007-07-14).
• Vector Calculus  by  Michael Jansson   (before 2007-07-13).
• Verizon gets out of the copper business  [1] by  Mark Ontkush  (2007-07-12).
• Unit for Planck's Constant  (in German)  by  Alex   (2007-07-06).
• Die Heisenbergsche Unschärferelation  (in German)  by  pgz  (bef. 2007-07-06).
• Perimeter of an ellipse  (using Adobe Illustrator)  by  Amy   (2007-07-05).
• Bohr coat of arms  by  Diane Kulisek   (2007-07-04).
• Counting without knowing how to count  by  Mathmate   (2007-07-02).
• Patt Hawkey's Math Links  at  Parks Junior High School   (bef. 2007-06-29).
• Counterfeit penny  [ mobile ]  by  Thaltgen   (before 2007-06-29).
• Heraldry Links  at  ForumRycerstwa  hosted by Yahoo!  (before 2007-06-19).
• Perimeter of an ellipse  by  Sam  at  UK Vintage Radio  (2007-06-18).
• Elliptic arc  by  Xeriar  (2007-06-17).
• Perfect Numbers, Mersenne Primes  by  Martin Gelbaum  (bef. 2007-06-13).
• Coat-of-arms of Karl Drais?  (in German)  by  Jochen Wilke  (2007-06-12).
• 1 is not a prime number  (in Romanian)  by  Lendar  (2007-06-10).
• Armigerous Scientists  at  Book of THoTH   by  MediaMonkey  (2007-06-07).
• Mathematical Magic  by  Byrd  (2007-06-06).
• Infamous Measurement Problem  by  sweatty_black_hole  (2007-05-24).
• Mathematical Humor  (update)  by  Scott Cram  (2007-05-24).
• Liczbach rzymskich:  Roman numerals, in Polish   (before 2007-05-24).
• Infinity Symbol Cloth  by  Lady Tricotine  (2007-05-21).
• Etymology of behen  by  Scion  (before 2007-05-21).
• Author of MathPages  by  Daniel Duparc  (2007-05-20).
• Coalescing black-hole binaries  by  Damour & Nagar  (2007-05-17).
• Infinite loops  by  Mike   (2007-05-15).
• Car speed  (in Romanian)  by  Victori   (2007-05-11).
• Elliptical orbit  by  Ilya   (2007-05-06).
• Gamma Function   Citizendium Article   (2007-05-05).
• Monkey Gravity  by  Yucha Yamaguchi   (2007-05-03).
• Centro Virtual de Divulgación de las Matemáticas   (before 2007-05-01).
• Additional Info  by  David Fawcette   at Columbia State  (bef. 2007-05-01).
• Symmetrical Polynomials  by  Francisco de Léon-Sotelo   (2007-04-29).
• Nautical mile?  by  smci   at "Yahoo! Answers"   (2007-04-28).
• Heraldry and Famous Coats of Arms  in  Symbolism  by  Mtsar  (2007-04-26).
• Archimedes  [ 2 ]   (before 2007-04-25).
• Mr. Miller makes the  Numericana Hall of Fame   (2007-04-25).
• Tycho Brahe's family...  by  Vacapinta  (2007-04-23).
• Mental Magic  at  magicpen.com  (before 2007-04-19).
• Review of Math Resources   in  I Like Math  Blog  (before 2007-04-19).
• Arms of Wernher von Braun  by  Ahnungslos  (2007-04-15).
• António Aniceto Monteiro  by  Jorge  (2007-04-14).
• Stemmi di scienziati  by  Sebastiano Pasquini  (before 2007-04-11).
• Algebra 2  (Fibonacci sharing)   at  The Morning Star Academy  (2007-04-11).
• Algebra 1  (Fibonacci sharing)   at  The Jubilee Academy  (2007-04-11).
• Perimeter of an Ellipse  at  Math Open Reference  (before 2007-04-11).
• Calculus Symbols  at  MathRamz.com  (2007-04-10).
• Mensa Sverige  Private forum, in Swedish  (2007-04-08).
• Galeria  (Polish) by  Karolina Alicja Kaszuba  (before 2007-04-08).
• Wappeneintrag  etc.  by  Dr. Frank Joachim Reuther  (before 2007-04-07).
• How many stars are there?  in  Sergiu M's Blog  (2007-04-05).
• Ships and Horizon  by  David A. Smith  (2007-04-02).
• Theorem of the Day  (related sites)  by  Robin Whitty   (before 2007-03-31).
• Vapen samlingar på internet  (Swedish)  by Awdaniec  (2007-03-26).
• The Kruskal Count  by  Sir Ross  (2007-03-26).
• Bimetallic Ratio  by  CJS  (2007-03-25).
• Vapen för berömda/kända/ökända personer  by  Marcus K  (2007-03-20).
• A Slice of Pi  by  Alex S.  (2007-03-15).
• Pi Day  and noteworthy constants...  by  Stephen Speicher  (2007-03-14).
• Quart of quarters  by  Squink  (2007-03-11).
• Stoichiometry of Black Powder  by  KevFla2001  (2007-03-03).
• Arms of Joseph Lister  by  Stephen J F Plowman  (2007-02-28).
• Arhimedova spirala  Bandwidth stealing  in Hungarian  (2007-02-23).
• Minimal surface bounding a given volume  by  Sydney Chivers  (2007-02-23).
• Heraldik för berömda/kända personer  by  Marcus Karlsson  (2007-02-19).
• Butylic and butyric  by  Porlock Junior  in Pharyngula blog (2007-02-18).
• Logaritma  (in Turkish) by  Eddie  (2007-02-15).
• Mathematics for Fun:   Eye Opener   (before 2007-02-10).
• Basic Trigonometry  by  Roy   (2007-02-07).
• Visconti, Sforza, Alfa-Romeo  (in Swedish) by  Awdaniec  (2007-02-01).
• Vapen för berömda personer  (in Swedish) by  Marcus K.  (2007-01-30).
• Metric value of a pound  (The AnswerBank) by  mibn2cweus  (2007-01-30).
• Ryedale's penny sorter  by  citizenkane  (around 2007-01-29).
• Perimeter of an ellipse   by  DrLaszloJamf  (2007-01-26).
• Carl von Weizsäcker   by  Norman Redington  (before 2007-01-26).
• Partition Function  by  Sam Kong   (2007-01-24).
• Counterfeit Coin Challenge   (2007-01-23).
• Cherish Freedom  in  Out From Under   (2007-01-18).
• Bereken de omtrek van een ellips  in  Dutch Wikipedia   (bef. 2007-01-17).
• Mathematical News  by  Umberto Cerruti  (before 2007-01-15).
• Black truss diamond markings  by  Schaula359   (2007-01-14).
• Coat-of-arms of Margaret Thatcher  by  Sean J. Murphy   (2007-01-11).
• K. Thomsen's formula for the surface area of an ellipsoid   (bef. 2007-01-11).
• Mathematical Magic Tricks   Everyone's bookmarks   (2007-01-09).
• The countability of rational numbers  by  Krusty   (2007-01-08).
• Horsepower  at  CycleChaos   (before 2007-01-06).
• Measurements & Units  at  Uncover the Net   (before 2007-01-03).
• SchoolNotes  of  Mr. Keeler,  Fort Walton Beach HS   (before 2007-01-03).
• Feynmann's way from Newton to Kepler by Brian Beckman (bef. 2006-12-31).
• Diffusion Quadratic Residues  by  RFZ_Quest  (2006-12-03).
• Tycho Brahe the Great Dane  by  Pmgisme  (2006-12-03).
• Kevin S. Brown, author of MathPages.com  by  Chris Hillman  (2006-12-02).
• Perimeter of an Ellipse  in  Dutch Wikipedia  (2006-12-01).
• Roman Numerals  by  CCC  (2006-11-30).
• Alchemical substances  [ 2 ]  by  Lokiyn  (2006-11-29).
• Epiphany and Humor  by  Mohan K.V  (2006-11-27).
• Three Prisoners Paradox  by  Scott Cram  (2006-11-26).
• Zoroastrian symbol in the Bible?   by  Seeker of Truth   (2006-11-22).
• Mathematics Links  by  Thomas Fink   (before 2006-11-22).
• Currency  by  Gaeleth   (2006-11-21).
• Mrs. Bennett's page of Links   Whitefish School District   (bef. 2006-11-21).
• The full 1089 force  by  Scott Cram  (2006-11-19).
• Mathematical abbreviation  ("Resp.")  by  Margaret Marks   (2006-11-18).
• "Insanely cool for math/language dorks"  by  Bynner  (2006-11-15).
• Fulminating Gold  by  JWB  in  Pepys' Diary  (2006-11-12).
• Signs, symbols and icons  by  Dave Gray  (before 2006-11-12).
• Harmonic series  in Physics 121  by  Corbin Covault  (2006-11-10).
• Tons galore...   in  Indonesian Wikipedia  (before 2006-10-31).
• Ideal gas law   at  www.squinch.org  (before 2006-10-30).
• Everything you ever wanted...   by  Marco Plumley  (bef. 2006-10-25).
• Subtractive principle in Roman numerals   by  akaSpider  (2006-10-23).
• Pound of pennies   by  JLam  (2006-10-22).
• U2 Puzzle  (Microsoft employement test)  by  Steveo1983   (2006-10-22).
• Infinity symbol  (Lemniscus)  by  Winhill  at UKC Forums  (2006-10-19).
• Dirichlet Beta Function   by  Gerson W. Barbosa  (2006-10-16).
• 7-11 puzzle as a homework assignment   by  CharlieLuciano  (2006-10-15).
• Weighing 12 coins   (in Lithuanian) by  Hoho  (2006-10-10).
• Omega constant  (in Swedish)  on  Wikipedia  (bef. 2006-10-08).
• Feet, meters or leagues  by  Jacquelyn, a.k.a. polar griff   (2006-10-04).
• Tycho Brahe's Shakespearean relatives  by  Banubula   (2006-10-01).
• Tycho Brahe's Shakespearean relatives  [ 1 ]  by  John Baez  (2006-10-01).
• Closing speed and Sagnac effect  by  Pupamancur  (2006-09-28).
• Weighing Marbles  by  Jwwells   (2006-09-23).
• Martin Luther King Jr. High School  by  Sharon Smith   (before 2006-09-16).
• Math 432, Fall 2006  by   Dr. Jim Haglund   (before 2006-09-15).
• Speed of light in a moving liquid  (Fizeau, 1851)   by   Montec   (2006-09-14).
• Websites related to Planck   by  Skwirlinator   (2006-09-10).
• Coat-of-arms of Wernher von Braun  on   Wikipedia   (bef. 2006-09-07).
• Combinatorial Game Theory  by  Richard J. Nowakowski  (bef. 2006-08-31).
• Lanczos approximation  on   Wikipedia   (bef. 2006-08-30).
• Teoría Electromagnética I  by  Ing. William Marín Moreno   (2006-08-26).
• Metrologist?  by  Dr. Russell J. Rowlett   (2006-08-10).
• Ramanujan and Ellipses  by  Ken Takusagawa   (2006-08-01).
• Distractions mathématiques  (in French)  by  Tropique   (2006-07-27).
• Speed of light in refractive media  by  tsmid, corrected by  przyk  (2006-07-25).
• Entropy and Maxwell's Demon  by  Franklyn   (2006-07-23).
• Counterfeit coin problem  by  TxHockeyGuy   (2006-07-02).
• L'énigme du barbier  [ 1 ]  by  Tropique   (2006-06-30).
• Chord, Height and Length  of an "elliptic bridge" by  Thurrdome  (2006-06-22).
• Math Course by Chris Fenwick, University College London (bef. 2006-06-18).
• Chinese Remainder Theorem   by  Mathmate  (2006-06-11).
• MathLinks   (in Romanian)   by  flip2004  (2006-06-04).
• Lose your marbles   by   pp-guest   (2006-06-02).
• Brain Teasers   by  Rita I. Carreira   (before 2006-05-21).
• World Science   edited by  Jack Lucentini   (2006-05-03).