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A q-analog of the Saalschütz theorem due to Jackson is given by where _3phi_2 is the q-hypergeometric function (Koepf 1998, p. 40; Schilling and Warnaar 1999).

In the plane, if a line intersects one side of a triangle and misses the three vertices, then it must intersect one of the other two sides. This is a special case of the ...

For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality: AB×CD+BC×DA>AC×BD. The Ptolemy inequality is still valid when ABCD is a triangular pyramid ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

The Bonne projection is a map projection that resembles the shape of a heart. Let phi_1 be the standard parallel, lambda_0 the central meridian, phi be the latitude, and ...

A class of map projections in which the parallels are represented by a system of non-concentric circular arcs with centers lying on the straight line representing the central ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

The study of a finite group G using the local subgroups of G. Local group theory plays a critical role in the classification theorem of finite groups.

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is ...