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cos(20 degrees)cos(40 degrees)cos(80 degrees)=1/8. An identity communicated to Feynman as a child by a boy named Morrie Jacobs (Gleick 1992, p. 47). Feynman remembered this ...

A magic square is said to be p-multimagic if the square formed by replacing each element by its kth power for k=1, 2, ..., p is also magic. A 2-multimagic square is called ...

Let a spherical triangle have sides a, b, and c with A, B, and C the corresponding opposite angles. Then (sin[1/2(A-B)])/(sin[1/2(A+B)]) = (tan[1/2(a-b)])/(tan(1/2c)) (1) ...

A near noble number is a real number 0<nu<1 whose continued fraction is periodic, and the periodic sequence of terms is composed of a string of p-1 1s followed by an integer ...

An obelisk is a stone pillar erected as a monument that usually consists of a pyramid atop a tall square (or sometimes rectangular base). The elongated square pyramid can ...

A number which is simultaneously octagonal and square. Let O_n denote the nth octagonal number and S_m the mth square number, then a number which is both octagonal and square ...

The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...

Ore algebra is an algebra of noncommutative polynomials representing linear operators for functional equations such as linear differential or difference equations. Ore ...

The surface of revolution of the parabola which is the shape used in the reflectors of automobile headlights (Steinhaus 1999, p. 242; Hilbert and Cohn-Vossen 1999). It is a ...

A multimagic square such that the first, second, third, fourth, and fifth powers of the elements all yield magic squares is known as a pentamagic square. The first known ...