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In 1638, Fermat proposed that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, and n n-polygonal numbers. ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...

There are a number of functions in mathematics commonly denoted with a Greek letter lambda. Examples of one-variable functions denoted lambda(n) with a lower case lambda ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

Let K_1^n and K_2^n be disjoint bicollared knots in R^(n+1) or S^(n+1) and let U denote the open region between them. Then the closure of U is a closed annulus S^n×[0,1]. ...

All triangles are bicentric, i.e., possess both an incircle and a circumcircle. This is not necessarily the case for polygons with four or more sides. The inradius r and ...

The only Wiedersehen surfaces are the standard round spheres. The conjecture was proven by combining the Berger-Kazdan comparison theorem with A. Weinstein's results for n ...

In 1976, Coates and Wiles showed that elliptic curves with complex multiplication having an infinite number of solutions have L-functions which are zero at the relevant fixed ...