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Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

A number of points on a line segment. The term was first used by Desargues (Cremona 1960, p. x). If the points A, B, C, ... lie on a line segment with the coordinates of the ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Consider the decimal expansion of the reciprocal of the number seven, 1/7=0.142857142857...=0.142857^_, (1) which is a repeating decimal. Now take overlapping pairs of these ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...