Mathematics and Physics Glossary

Ice machine (Phys.), a machine for making ice artificially, as by the production of a low temperature through the sudden expansion of a gas or vapor, or the rapid evaporation of a volatile liquid.

Icosahedral a. (Geom.) Having twenty equal sides or faces.

Icosahedron n. (Geom.) A solid bounded by twenty sides or faces.

Ideal, a. (Math.) Imaginary.

Identical equation (Math.), an equation which is true for all values of the algebraic symbols which enter into it.

Identity, n.; pl. Identities. (Math.) An equation that is satisfied by any number that replaces the variable for which the equation is defined.

-- Identity element, n. (Math.) The element of a set of numbers that when combined with another number in an operation leaves that number unchanged. For example, 0 is the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Similarly, 1 is the identity element under multiplication for the real numbers, since a × 1 = 1 × a = a. Also called unity.

-- Identity matrix, n. (Math.) (Math.) A square matrix with numeral 1's along the diagonal from upper left to lower right and 0's in all other positions.