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Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...

The Clebsch diagonal cubic is a cubic algebraic surface given by the equation x_0^3+x_1^3+x_2^3+x_3^3+x_4^3=0, (1) with the added constraint x_0+x_1+x_2+x_3+x_4=0. (2) The ...

An Enriques surface X is a smooth compact complex surface having irregularity q(X)=0 and nontrivial canonical sheaf K_X such that K_X^2=O_X (Endraß). Such surfaces cannot be ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

A superior highly composite number is a positive integer n for which there is an e>0 such that (d(n))/(n^e)>=(d(k))/(k^e) for all k>1, where the function d(n) counts the ...

An unknown is an independent variable of a function. A function with n independent variables is said to be a function "in," "with," or "of" n unknowns.

where _2F_1(a,b;c;z) is a hypergeometric function and _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function.

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...