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Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...

The great stellated dodecahedron is one of the Kepler-Poinsot polyhedra. It is also the uniform polyhedron with Maeder index 52 (Maeder 1997), Wenninger index 22 (Wenninger ...

No A is not-A.

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).

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 metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area K = (a^2sinBsinC)/(2sinA) (1) = (a^2sinBsin(pi-A-B))/(2sinA). (2) The third ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...