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The dilogarithm identity Li_2(-x)=-Li_2(x/(1+x))-1/2[ln(1+x)]^2.

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

For a logarithmic spiral with parametric equations x = e^(bt)cost (1) y = e^(bt)sint, (2) the involute is given by x = (e^(bt)sint)/b (3) y = -(e^(bt)cost)/b, (4) which is ...

The winding number W(theta) of a map f(theta) with initial value theta is defined by W(theta)=lim_(n->infty)(f^n(theta)-theta)/n, which represents the average increase in the ...

A measure space is a measurable space possessing a nonnegative measure. Examples of measure spaces include n-dimensional Euclidean space with Lebesgue measure and the unit ...

The metabidiminished icosahedron is a convex equilateral solid that is Johnson solid J_(62). The unit metabidiminished icosahedron has volume V=1/6(5+2sqrt(5)) (1) and Dehn ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

Spherical triangles into which a sphere is divided by the planes of symmetry of a uniform polyhedron.

The Mollweide projection is a map projection also called the elliptical projection or homolographic equal-area projection. The forward transformation is x = ...

The symbol × used to denote multiplication, i.e., a×b denotes a times b. The symbol × is also used to denote a group direct product, a Cartesian product, or a direct product ...