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Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

A self-intersecting minimal surface which can be generated using the Enneper-Weierstrass parameterization with f(z) = 1 (1) g(z) = zeta. (2) Letting z=re^(iphi) and taking ...

There are two theorems commonly known as Feuerbach's theorem. The first states that circle which passes through the feet of the perpendiculars dropped from the polygon ...

The Gegenbauer polynomials C_n^((lambda))(x) are solutions to the Gegenbauer differential equation for integer n. They are generalizations of the associated Legendre ...

A root-finding method which was among the most popular methods for finding roots of univariate polynomials in the 19th and 20th centuries. It was invented independently by ...

A graph H is a minor of a graph G if a copy of H can be obtained from G via repeated edge deletion and/or edge contraction. The Kuratowski reduction theorem states that any ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the ...