257-gon

In geometry, a 257-gon (diacosipentacontaheptagon, diacosipentecontaheptagon) is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 91800°.

Regular 257-gon

The area of a regular 257-gon is (with t = edge length)

A whole regular 257-gon is not visually discernible from a circle, and its perimeter differs from that of the circumscribed circle by about 24 parts per million.

Construction

The regular 257-gon (one with all sides equal and all angles equal) is of interest for being a constructible polygon: that is, it can be constructed using a compass and an unmarked straightedge. This is because 257 is a Fermat prime, being of the form 2²ⁿ + 1 (in this case n = 3). Thus, the values and are 128-degree algebraic numbers, and like all constructible numbers they can be written using square roots and no higher-order roots.

Although it was known to Gauss by 1801 that the regular 257-gon was constructible, the first explicit constructions of a regular 257-gon were given by Magnus Georg Paucker (1822) and Friedrich Julius Richelot (1832). Another method involves the use of 150 circles, 24 being Carlyle circles: this method is pictured below. One of these Carlyle circles solves the quadratic equation x² + x − 64 = 0.

GON

Gon or GON may refer to:

Fiction

Gon (manga)

Gon (Japanese: ゴン) is a tiny fictional dinosaur and the title character of a Japanese manga series created by Masashi Tanaka. The Gon series features the completely wordless adventures of the irascible title character as he interacts with the natural world, depicted by Tanaka in lush, realistic detail. Gon somehow survived the extinction of his fellow dinosaurs and interacts with paleolithic animals.

Gon was most notable outside Japan for his appearance in the PlayStation version of Tekken 3. An animated TV series began airing in Japan on April 2, 2012. In 1998, the manga received an Excellence Prize at the Japan Media Arts Festival.

Characteristics

Gon's exact saurian species is never delved into. He vaguely resembles an outdated depiction of a generic carnosaur in a tripod stance, only about the size of a small dog. He is an omnivore with an enormous appetite. He possesses enormous power and endurance for his size, his feats of strength including supporting his own weight with his jaws, to being able to partially lift a fully grown African Elephant. His scaly hide is almost impenetrable, being able to shrug off the bites of larger predators..

Gon, Burkina Faso

Gon, Burkina Faso is a village in the Zabré Department of Boulgou Province in south-eastern Burkina Faso. As of 2005, the village has a population of 810.

References