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Thomae's theorem, also called Thomae's transformation, is the generalized hypergeometric function identity (1) where Gamma(z) is the gamma function, _3F_2(a,b,c;e,f;z) is a ...

In the 1980s, Samuel Yates defined a titanic prime to be a prime number of at least 1000 decimal digits. The smallest titanic prime is 10^(999)+7. As of 1990, more than 1400 ...

A toroidal polyhedron is a polyhedron with genus g>=1 (i.e., one having one or more holes). Examples of toroidal polyhedra include the Császár polyhedron and Szilassi ...

The simple process of voting leads to surprisingly counterintuitive paradoxes. For example, if three people vote for three candidates, giving the rankings A, B, C; B, C, A; ...

A Wilson prime is a prime satisfying W(p)=0 (mod p), where W(p) is the Wilson quotient, or equivalently, (p-1)!=-1 (mod p^2). The first few Wilson primes are 5, 13, and 563 ...

A knot property, also called the twist number, defined as the sum of crossings p of a link L, w(L)=sum_(p in C(L))epsilon(p), (1) where epsilon(p) defined to be +/-1 if the ...

The von Staudt-Clausen theorem, sometimes also known as the Staudt-Clausen theorem (Carlitz 1968), states that B_(2n)=A_n-sum_(p_k; (p_k-1)|2n)1/(p_k), (1) where B_(2n) is a ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

The Costa surface is a complete minimal embedded surface of finite topology (i.e., it has no boundary and does not intersect itself). It has genus 1 with three punctures ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...