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The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n=(9cos^2omega+52cosomega+44)/(36n^2sin^2omega), (1) where omega=2pi/n (Alikoski 1939; ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

The rectangle function Pi(x) is a function that is 0 outside the interval [-1/2,1/2] and unity inside it. It is also called the gate function, pulse function, or window ...

A process of successively crossing out members of a list according to a set of rules such that only some remain. The best known sieve is the sieve of Eratosthenes for ...

The diagonal slash "/" used as the bar between numerator and denominator of an in-line fraction (Bringhurst 1997, p. 284). The solidus is also called a diagonal. Special care ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...