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The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

An (n,k) fountain is an arrangement of n coins in rows such that exactly k coins are in the bottom row and each coin in the (i+1)st row touches exactly two in the ith row. ...

The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

A grid usually refers to two or more infinite sets of evenly-spaced parallel lines at particular angles to each other in a plane, or the intersections of such lines. The two ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

A type of number involving the roots of unity which was developed by Kummer while trying to solve Fermat's last theorem. Although factorization over the integers is unique ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...