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Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula chi(g)=V-E+F, (1) where chi(g)=2-2g (2) is the Euler characteristic, ...

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

A minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v) (1) y(u,v) = ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

The norm of a mathematical object is a quantity that in some (possibly abstract) sense describes the length, size, or extent of the object. Norms exist for complex numbers ...