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A regular pyramid is a right pyramid whose base is a regular polygon. For a right pyramid of height h with a regular n-gonal base of side length a and circumradius R, the ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

A function f is Carathéodory differentiable at a if there exists a function phi which is continuous at a such that f(x)-f(a)=phi(x)(x-a). Every function which is Carathéodory ...

The inverse curve of the circle with parametric equations x = acost (1) y = asint (2) with respect to an inversion circle with center (x,y) and radius R is given by x_i = ...