pentacosiagon

A pentacosiagon is a polygon with 500 sides. The term is derived from Greek roots: "penta" meaning five, "kosioi" meaning two hundred, and "gonia" meaning angle. Therefore, pentacosiagon literally translates to "five hundred angled". In Euclidean geometry, a regular pentacosiagon has all sides of equal length and all interior angles equal. The sum of the interior angles of any pentacosiagon, regular or irregular, is given by the formula (n-2) * 180 degrees, where n is the number of sides. For a pentacosiagon, this sum is (500-2) * 180 = 498 * 180 = 89,640 degrees. The measure of each interior angle in a regular pentacosiagon is 89,640 / 500 = 179.28 degrees. Similarly, the exterior angle of a regular pentacosiagon is 360 / 500 = 0.72 degrees. Due to its large number of sides, a regular pentacosiagon appears very close to a circle. Its construction using only a compass and straightedge is not possible, as 500 is not a product of distinct Fermat primes and a power of 2.