Mathematics and Physics Glossary

Half-integral, a. (Math.) A fraction that has an integer as a numerator and 2 as a denominator.

Half-life, n. (Phys.) The time required for half the nuclei in a sample of a specific isotopic species to undergo radioactive decay.

Half-line, n. (Math.) See Ray.

Half-ray n. (Geom.) A straight line considered as drawn from a center to an indefinite distance in one direction, the complete ray being the whole line drawn to an indefinite distance in both directions.

Hamiltonian, n. (Phys.) [Invented by Sir William Rowan Hamilton (1805-1865), Irish mathematician.] A mathematical function that can be used systematically and with great generality to generate the equations of motion of a dynamic system, equal for many such systems to the sum of the kinetic and potential energies of the system expressed in terms of the system's coördinates and momenta treated as independent variables.

Hamiltonian walk, n. (Math.) a path traced out on a topological graph which visits every vertex once and once only, except possibly for the start and finish, which might be on the same vertex.

Happy numbers, n. (Math.) A number has all its digits squared and added together to make a new number. This process is repeated until a 1 is obtained, at which point the original number is described as happy. If a 1 is never obtained, the original number is said to be sad.