Polygon
In elementary geometry, a polygon /ˈpɒlɪɡɒn/ is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body. An n-gon is a polygon with n sides. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.
The basic geometrical notion of a polygon has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the bounding closed polygonal chain and with simple polygons which do not self-intersect, and they often define a polygon accordingly. A polygonal boundary may be allowed to intersect itself, creating star polygons. Geometrically two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments may be considered parts of a single edge; however mathematically, such corners may sometimes be allowed. These and other generalizations of polygons are described below.
Polygon (film)
Polygon or Firing Range (Russian: Полигон) is a 1977 Soviet animation science fiction short film.
Plot summary
The plot is based on an anti-war military science fiction story by Sever Gansovsky.
In the not-too-distant future a scientist from a military great power wants revenge for his son (who was a soldier KIA during war) and thus invents a weapon capable of ending the conflict - an automated mind-reading tank that detects and reacts to human feelings of hostility and fear. After his revenge successfully takes place (as the tank destroys a number of generals responsible for the loss of his son) he himself falls victim to his own creation.
The film has an open ending.
Voice cast
Production Information
Polygon was directed by Anatoly Petrov (born 1937) and it was based on a screenplay by Sever Gansovsky (edited by Arcady Snessarev). The short film was produced by Lubov' Butyrina and released by Soyuzmultfilm studio. It featured the artwork of artists Elena Karavaeva, Olga Bogolubova, I. Kulakova, Elena Bogolubova and N. Ivancheva. The art director was Galina Barinova.
Polygon (disambiguation)
Polygon may refer to:
In mathematics and computing:
other meanings:
Symmetry (disambiguation)
Symmetry may refer to:
In science and mathematics:
In arts and entertainment:
Other uses:
Symmetry (horse)
Symmetry (foaled 1795) was a British Thoroughbred racehorse and sire best known for winning the classic St Leger Stakes in 1798. Originally trained in Yorkshire won the St Leger at Donacaster on his final appearance as a three-year-old and when on to defeat the Epsom Derby winner Sir Harry in a match race at York in the following year. As a five-year-old he was transferred to race at Newmarket where he lost a rematch with Sir Harry, but won his three remaining races, including matches against Sorcerer and Diamond, two of the leading racehorss of the time. After his retirement from racing, Symmetry was sold and exported to stand as a breeding stallion in Russia.
Background
Symmetry was a grey horse bred by his owner Sir Thomas Gascoigne, 8th Baronet. His sire Delpini, from whom he inherited his colour, was a successful rachorse who won eight consecutive races at Newmarket in 1786 and 1787, before becoming a leading sire in the north of England. His stock were particularly noted for their stamina. Symmetry's dam Violet, also bred by Gascoigne, was a highly successful broodmare who also produced the Oaks winner Theophania (by Delpini) and Golden Locks, the dam of Soothsayer. Symmetry was the third of fourteen foals produced by Violet between 1793 and 1807.
Nonagon
In geometry, a nonagon /ˈnɒnəɡɒn/ (or enneagon /ˈɛniːəɡɒn/) is a nine-sided polygon or 9-gon.
The name "nonagon" is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek enneagonon (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct, though somewhat less common than "nonagon".
Regular nonagon
A regular nonagon is represented by Schläfli symbol {9} and has internal angles of 140°. The area of a regular nonagon of side length a is given by
where the radius r of the inscribed circle of the regular nonagon is
and where R is the radius of its circumscribed circle:
Construction
Although a regular nonagon is not constructible with compass and straightedge (as 9 = 32, which is not a product of distinct Fermat primes), there are very old methods of construction that produce very close approximations. It can be also constructed using neusis, or by allowing the use of an angle trisector.
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