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Since |(a+ib)(c+id)| = |a+ib||c+di| (1) |(ac-bd)+i(bc+ad)| = sqrt(a^2+b^2)sqrt(c^2+d^2), (2) it follows that (a^2+b^2)(c^2+d^2) = (ac-bd)^2+(bc+ad)^2 (3) = e^2+f^2. (4) This ...

Consider a symmetric triangle wave T(x) of period 2L. Since the function is odd, a_0 = 0 (1) a_n = 0, (2) and b_n = (3) = (32)/(pi^2n^2)cos(1/4npi)sin^3(1/4npi) (4) = ...

Two geometric figures are said to exhibit geometric congruence (or "be geometrically congruent") iff one can be transformed into the other by an isometry (Coxeter and ...

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...

The cube of a graph is defined as its third graph power.

The dual of the great truncated cuboctahedron U_(20) and Wenninger dual W_(93).

800 The dual of the great rhombidodecahedron U_(73) and Wenninger dual W_(109).

A dozen dozen, or the square number 144.

A n-gonal cupola adjoined to a 2n-gonal antiprism.

The largest unit fraction, 1/2. 1/2 is a rational number with terminating decimal expansion 0.5.