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A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

Abel's integral is the definite integral I = int_0^infty(tdt)/((e^(pit)-e^(-pit))(t^2+1)) (1) = 1/2int_(-infty)^infty(tdt)/((e^(pit)-e^(-pit))(t^2+1)) (2) = ...

Condorcet's jury theorem states that given a group of voters (a "jury") independently choosing by majority vote between a correct outcome with probability 0<=p<=1 and an ...

A connection between two or more vertices of a hypergraph. A hyperedge connecting just two vertices is simply a usual graph edge.