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The Bernoulli numbers B_n are a sequence of signed rational numbers that can be defined by the exponential generating function x/(e^x-1)=sum_(n=0)^infty(B_nx^n)/(n!). (1) ...

Two losing gambling games can be set up so that when they are played one after the other, they become winning. There are many ways to construct such scenarios, the simplest ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. Two other ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

In general, an icosidodecahedron is a 32-faced polyhedron. A number of such solids are illustrated above. "The" (quasiregular) icosidodecahedron is the 32-faced Archimedean ...

A magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube. A magic tesseract has magic constant ...

The quartic with implicit equation x^4=x^2y-y^3. (1) The bow has vertical tangents at (+/-2/9sqrt(3),2/9) and horizontal tangents at (+/-1/4sqrt(2),1/4). Its curvature is ...

Two quantities are said to be different (or "unequal") if they are not equal. The term "different" also has a technical usage related to modules. Let a module M in an ...

Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...