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A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

Let alpha and beta be any ordinal numbers, then ordinal exponentiation is defined so that if beta=0 then alpha^beta=1. If beta is not a limit ordinal, then choose gamma such ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

An interpolation formula, sometimes known as the Newton-Bessel formula, given by (1) for p in [0,1], where delta is the central difference and B_(2n) = 1/2G_(2n) (2) = ...

A box integral for dimension n with parameters q and s is defined as the expectation of distance from a fixed point q of a point r chosen at random over the unit n-cube, ...

Any row r and column s of a determinant being selected, if the element common to them be multiplied by its cofactor in the determinant, and every product of another element ...

Conway triangle notation defines S=2Delta (1) where Delta is the area of a reference triangle, and S_phi=Scotphi. (2) This gives the special cases S_A = 1/2(-a^2+b^2+c^2) (3) ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...