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The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge: 1. circle squaring. 2. cube duplication. 3. ...

"Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges. The terms "point," "junction," ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

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 ...

Buffon's needle problem asks to find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines a distance d apart. The ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...