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The Sierpiński gasket graph of order n is the graph obtained from the connectivity of the Sierpiński sieve. The first few Sierpiński gasket graphs are illustrated above. S_2 ...

Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

The Euler-Mascheroni constant gamma, sometimes also called 'Euler's constant' or 'the Euler constant' (but not to be confused with the constant e=2.718281...) is defined as ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...