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The pentaflake is a fractal with 5-fold symmetry. As illustrated above, five pentagons can be arranged around an identical pentagon to form the first iteration of the ...

Plouffe's constants are numbers arising in summations of series related to r_n=f(2^n) where f is a trigonometric function. Define the Iverson bracket function rho(x)={1 for ...

The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...

The most common "sine integral" is defined as Si(z)=int_0^z(sint)/tdt (1) Si(z) is the function implemented in the Wolfram Language as the function SinIntegral[z]. Si(z) is ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

A string figure is any pattern produced when a looped string is spanned between two hands and is twisted and woven in various manners around the fingers and the wrists. The ...