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A triangle center function (sometimes simply called a center function) is a nonzero function f(a,b,c) that is homogeneous f(ta,tb,tc)=t^nf(a,b,c) (1) bisymmetry in b and c, ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b ...

Specifying two adjacent side lengths a and c of a triangle (with a<c) and one acute angle A opposite a does not, in general, uniquely determine a triangle. If sinA<a/c, there ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

The atom-spiral, also known as the atomic spiral, is the curve with polar equation r=theta/(theta-a) for a real parameter a (van Maldeghem 2002). When theta is allows to vary ...

The bigyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(79). The unit bigyrate diminished rhombicosidodecahedron has volume ...

The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Define the angles theta and phi by letting a=cos(theta/2) and ...