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Let a triangle have side lengths a, b, and c with opposite angles A, B, and C. Then (b+c)/a = (cos[1/2(B-C)])/(sin(1/2A)) (1) (c+a)/b = (cos[1/2(C-A)])/(sin(1/2B)) (2) ...

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...

A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

Any prime number other than 2 (which is the unique even prime). Humorously, 2 is therefore the "oddest" prime.

The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...

A popular acronym for "principal ideal domain." In engineering circles, the acronym PID refers to the "proportional-integral-derivative method" algorithm for controlling ...

The fraction eta of a volume filled by a given collection of solids.

The Pappus spiral is the name given to the conical spiral with parametric equations x(t) = asin(alphat)cost (1) y(t) = asin(alphat)sint (2) x(t) = acos(alphat) (3) by ...

The pentagrammic deltohedron (Har'El 1993) is the dual polyhedron of the pentagrammic antiprism U_(79).