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There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where zeta(z,a) is a ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following ...

The Miquel point is the point of concurrence of the Miquel circles. It is therefore the radical center of these circles. Let the points defining the Miquel circles be ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

A surface such as the Möbius strip or Klein bottle (Gray 1997, pp. 322-323) on which there exists a closed path such that the directrix is reversed when moved around this ...

A "squashed" spheroid for which the equatorial radius a is greater than the polar radius c, so a>c (called an oblate ellipsoid by Tietze 1965, p. 27). An oblate spheroid is a ...

A prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called ...

A polyhedron is rigid if it cannot be continuously deformed into another configuration. A rigid polyhedron may have two or more stable forms which cannot be continuously ...