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If the Taniyama-Shimura conjecture holds for all semistable elliptic curves, then Fermat's last theorem is true. Before its proof by Ribet in 1986, the theorem had been ...

A formal extension of the hypergeometric function to two variables, resulting in four kinds of functions (Appell 1925; Picard 1880ab, 1881; Goursat 1882; Whittaker and Watson ...

Analysis

A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...

The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius b<a, where a is the radius of a rolling circle. Curtate ...

The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric problems of antiquity, in ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...