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The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

The number of regions into which space can be divided by n mutually intersecting spheres is N=1/3n(n^2-3n+8), giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

The problem of finding in how many ways E_n a plane convex polygon of n sides can be divided into triangles by diagonals. Euler first proposed it to Christian Goldbach in ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon. If each point of intersection is associated with a node and diagonals are split ar each ...

Direct search factorization is the simplest (and most simple-minded) prime factorization algorithm. It consists of searching for factors of a number by systematically ...

(1) Based on or involving trial and error. (2) Convincing without being rigorous.

The primes with Legendre symbol (n/p)=1 (less than N=pi(d) for trial divisor d) which need be considered when using the quadratic sieve factorization method.

A prime factorization algorithm in which a sequence of trial divisors is chosen using a quadratic sieve. By using quadratic residues of N, the quadratic residues of the ...