Centagons

A centagon is a polygon with 100 sides and 100 vertices. The term is derived from the Greek word "kenton" meaning "hundred". Like all polygons, a centagon can be convex or concave, regular or irregular. A regular centagon has all sides of equal length and all interior angles equal.

The sum of the interior angles of any polygon can be calculated using the formula (n-2) * 180 degrees, where n is the number of sides. For a centagon, this sum is (100-2) * 180 = 98 * 180 = 17640 degrees. In a regular centagon, each interior angle measures 17640 / 100 = 176.4 degrees. The exterior angle of a regular centagon is 360 / 100 = 3.6 degrees.

While it is theoretically possible to construct a regular centagon using only a compass and straightedge, it is not a constructible polygon by these methods alone. This is because the number of sides, 100, is not a product of distinct Fermat primes. Nevertheless, regular centagons can be approximated or constructed using tools beyond the compass and straightedge, such as a marked ruler (neusis construction).

Centagons appear in various abstract mathematical contexts, but they are not commonly encountered in everyday geometry or architecture due to their high number of sides and the complexity of their precise construction.