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A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

A geodesic on a paraboloid x = sqrt(u)cosv (1) y = sqrt(u)sinv (2) z = u (3) has differential parameters defined by P = ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...

The golden ratio phi can be written in terms of a nested radical in the beautiful form phi=sqrt(1+sqrt(1+sqrt(1+sqrt(1+...)))), (1) which can be written recursively as ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...

A skewed distribution which is similar to the binomial distribution when p!=q (Abramowitz and Stegun 1972, p. 930). y=k(t+A)^(A^2-1)e^(-At), (1) for t in [0,infty) where A = ...

The pentagonal antiprism is the antiprism having a regular pentagon for the top and bottom bases. It is also the uniform polyhedron with Maeder index 77 (Maeder 1997) and ...

A pentagonal pyramid is pyramid having a pentagonal base. The edge length e and slant height s of a pentagonal pyramid with regular base of side length a are given by e = ...

A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers ...

A number which is simultaneously a pentagonal number P_n and a square number S_m. Such numbers exist when 1/2n(3n-1)=m^2. (1) Completing the square gives ...