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The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

There are two definitions of the Fermat number. The less common is a number of the form 2^n+1 obtained by setting x=1 in a Fermat polynomial, the first few of which are 3, 5, ...

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...