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Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...

The endodocehedron, also called the concave pyrohedral dodecahedron, is the concave solid corresponding to the interior void formed when each face of a regular dodecahedron ...

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with ...

An equilateral polygon is a polygon whose edges are all of equal length (Williams 1979, pp. 31-32). The most prominent examples of equilateral polygons are the regular ...

When applied to a system possessing a length R at which solutions in a variable r change character (such as the gravitational field of a sphere as r runs from the interior to ...

In the above figure, the sides a and b have the same length, appearances to the contrary. In the related illusion illustrated above, the interior lines appear to be of ...

Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as ...

A ring torus constructed out of a square of side length c can be dissected into two squares of arbitrary side lengths a and b (as long as they are consistent with the size of ...