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A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

A chordless cycle of a graph G is a graph cycle in G that has no cycle chord. Unfortunately, there are conflicting conventions on whether or not 3-cycles should be considered ...

A game described by Scarne which is played on a 5×5 board by two players who alternate placing, one at a time, their four counters each, after which the counters are moved ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...

In a given triangle DeltaABC with all angles less than 120 degrees (2pi/3, the first Fermat point X or F_1 (sometimes simply called "the Fermat point," Torricelli point, or ...