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A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the ...

A pairing function is a function that reversibly maps Z^*×Z^* onto Z^*, where Z^*={0,1,2,...} denotes nonnegative integers. Pairing functions arise naturally in the ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

An integer m such that if p|m, then p^2|m, is called a powerful number. There are an infinite number of powerful numbers, and the first few are 1, 4, 8, 9, 16, 25, 27, 32, ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...