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# Topic: Polygon

###### In the News (Tue 23 Apr 19)

 SparkNotes: Polygons: Defining a Polygon A polygon is one type of simple closed curve. A polygon is the union of three or more line segments whose endpoints meet. The segments are called the sides of the polygon. www.sparknotes.com /math/geometry1/polygons/section1.html   (479 words)

 Polygon - LoveToKnow 1911 The term regular polygon is usually restricted to "convex" polygons; a special class of polygons (regular in the wider sense) has been named "star polygons" on account of their resemblance to star-rays; these are, however, concave. The Arabian geometers of the 9th century showed that the heptagon required the solution of a cubic equation, thus resembling the Pythagorean problems of "duplicating the cube" and "trisecting an angle." Edmund Halley gave solutions for the heptagon and nonagon by means of the parabola and circle, and by a parabola and hyperbola respectively. In general, the number of star polygons which can be drawn with the vertices of an n-point regular polygon is the number of numbers which are not factors of n and are less than In. www.1911encyclopedia.org /Polygon   (1465 words)

 Polygon - Wikipedia, the free encyclopedia If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary. Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. Equiangular polygon: a polygon whose vertex angles are equal (Williams 1979, p. en.wikipedia.org /wiki/Polygon   (976 words)

 PlanetMath: polygon A polygonal curve is a simple closed path consisting of a finite sequence of coplanar points together with each open interval determined by two consecutive points on the path. A polygon is a set homeomorphic to the closed unit disc whose boundary is a finite union of line segments. A polygon is a 2-dimensional polytope (not necessarily convex). planetmath.org /encyclopedia/Polygon.html   (376 words)

 Polygon - MSN Encarta These restrictions require that the sides of a polygon not cross each other and that pairs of sides intersect at their endpoints, which are called vertices. All polygons have an equal number of sides and vertices, and the sum of the interior angles of a polygon with n sides is 180° × (n – 2). Every interior angle of a convex polygon is less than 180°, while at least one angle of a concave polygon is greater than 180°. encarta.msn.com /encnet/refpages/RefArticle.aspx?refid=761553849   (282 words)

 Vicon | Products | Software | Polygon Polygon allows you to import all the common data generated by a motion measurement session as well as other reference data such as text files, data tables, AVI files, pictures and even web pages. Polygon allows any report to be saved as a template, which means that exactly the same report can be generated in seconds based on a different data set. The interactive, hyperlink-based Polygon reports are ideal for presenting data – whether it is for a conference, a referring physician, a college audience or maybe just for an internal analysis session. www.vicon.com /products/polygon.html   (648 words)

 Polygon (computer graphics) - Wikipedia, the free encyclopedia Polygons are used in computer graphics to compose images that are three-dimensional in appearance. Usually (but not always) triangular, polygons arise when an object's surface is modeled, vertices are selected, and the object is rendered in a wire frame model. This is quicker to display than a shaded model; thus the polygons are a stage in computer animation. en.wikipedia.org /wiki/Polygon_(computer_graphics)   (170 words)

 Perimeter The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units. The perimeter of this yard is the distance around the outside of the yard, indicated by the red arrow; It is measured in linear units such as feet or meters. www.mathgoodies.com /lessons/vol1/perimeter.html   (587 words)

 Polygons - Polygon basics - First Glance   (Site not responding. Last check: ) Polygons are named according to the number of sides and angles they have. The most familiar polygons are the triangle, the rectangle, and the square. Polygons also have diagonals, which are segments that join two vertices and are not sides. www.math.com /school/subject3/lessons/S3U2L1GL.html   (83 words)

 Polygon definition - Math Open Reference Polygons are one of the most all-encompassing shapes in geometry. The interior angles of a polygon are those angles at each vertex on the inside of the polygon. The apothem of a polygon is a line from the center to the midpoint of a side. www.mathopenref.com /polygon.html   (491 words)

 PlanetMath: regular polygon In ordinary usage, a regular polygon is a convex polygon with all its sides equal and all its angles equal, that is, a polygon that is both equilateral and equiangular. Any regular polygon can be inscribed into a circle and a circle can be inscribed within it. This is version 10 of regular polygon, born on 2002-02-19, modified 2006-11-03. planetmath.org /encyclopedia/RegularPolygon.html   (347 words)

 Star polygon: Facts and details from Encyclopedia Topic   (Site not responding. Last check: ) A polygon (literally "many angle", see wiktionary for the etymology) is a closed plane (mathematics)planar path composed of a finite number of sequential line... A complex star polygon can be obtained by rotating these regular n/x-gons one vertex to the left on the original polygon until the number of vertices rotated equals n/x minus one. (a heptadecagon (or 17-gon) is a seventeen-sided polygon.... www.absoluteastronomy.com /encyclopedia/s/st/star_polygon.htm   (1214 words)

 [No title] A polygon with 5 edges is called a pentagon, one with 6 edges is a hexagon and so on (using greek numbering). Convex polygons have the property that a line drawn from any point on the boundary of the polygon to any other point on the boundary of the same polygon will never cross another edge of the polygon. The third algorithm is the constrained approximation and the fourth algorithm uses algorithms 2 and 3 to approximate a polygon (the min-# problem). www.lycos.com /info/polygon.html   (573 words)

 Polygon Summary   (Site not responding. Last check: ) Polygons are named to indicate the number of their sides or number of noncollinear points present in the polygon. If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary. Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. www.bookrags.com /Polygon   (1346 words)

 Totally Tessellated: Polygons and Angles Polygons are named according to their number of line segments, or sides. An important property of polygons is that all polygons with the same number of sides have the same sum of interior angle Thus, the interior angle sum of a polygon with n sides is 180°(n-2). library.thinkquest.org /16661/background/polygons.html   (330 words)

 Polygon - Wikinfo A polygon (from the Greek poly, for "many", and gwnos, for "angle") is a closed planar path composed of a finite number of straight line segments. Polygons are named according to the number of sides, combining a Greek root with the suffix -gon, e.g. A concyclic or cyclic polygon is a polygon whose vertices all lie on a single circle. www.wikinfo.org /wiki.php?title=Polygon   (2845 words)

 Polygons The line segments are called the sides of the polygon, and the points at which they intersect are called vertices. Polygons are classified according to the number of sides they have. It should be recognisable at this stage that polygons surround us in our every day lives whether it be the face of the computer screen that you are looking at right now or the shape of the matt that your mouse rolls on. www.ul.ie /~cahird/polyhedronmode/polygons.htm   (169 words)

 polygon. The Columbia Encyclopedia, Sixth Edition. 2001-05 In a regular polygon the sides are of equal length and meet at equal angles; all other polygons are not regular, although either their sides or their angles may be equal, as in the cases of the rhombus and the rectangle. The simplest regular polygons are the equilateral triangle, the square, the regular pentagon (of 5 sides), and the regular hexagon (of 6 sides). The first five regular polygons with a prime number of sides that can be constructed using a straightedge and compass have 3, 5, 17, 257, and 65,537 sides. www.bartleby.com /65/po/polygon.html   (275 words)

 Regular polyhedra A polygon whose vertices all belong to a single plane is called planar. Polygons are often identified with their interior regions. For a polygon it means that every closed curve in its interior can be continuously shrunk into a point while the deformation is being carried entirely inside the polygon. www.cut-the-knot.org /do_you_know/polyhedra.shtml   (1157 words)

 Figures and polygons A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a parallelogram is 360 degrees. www.mathleague.com /help/geometry/polygons.htm   (620 words)

 softWoRx Help: Edit Polygon These polygons can be used either to define 3D structure in another program or to cut out a portion of an image defined by the polygons. Polygons are "manually" created by defining polygon points with clicks of the left mouse button in the image window. Once the initial polygon is made, it may have some sharp edges where the edge of the structure was missed. www.indiana.edu /~elegans/Deconv/EditPolygon.html   (1904 words)

 Point in Polygon Strategies The polygon is treated as a fan of triangles emanating from one vertex and the point is tested against each triangle by computing its barycentric coordinates. The bounding box surrounding the polygon is split into a number of horizontal bins and the parts of the edges in a bin are kept in a list, sorted by the minimum X component. Random polygons tend to be somewhat unlikely (no one ever uses 1000 edge random polygons for anything except testing), while regular polygons are more orderly than a "typical" polygon; normal behavior tends to be somewhere in between. www.acm.org /pubs/tog/editors/erich/ptinpoly   (4418 words)

 Polygons A diagonal of a polygon is a segment that joins two non consecutive vertices. If the diagonals of a polygon is drawn from one vertex, then the sum of the measures of the angles of the polygon can be calculated. A regular polygon is a polygon that is both equilateral and equiangular. library.thinkquest.org /10030/6poly.htm   (161 words)

 Polygon Puzzler A planar polygon is a polygon whose vertices all lie in the same plane. That is, although the vertices of the polygon lie in some two-dimensional plane, the vertices are specified in three-dimensional Cartesian coordinates. The output should be the area of the polygons specified by the input and should be rounded to the nearest 1/1000 (i.e., three places after the decimal point should be printed). acm.uva.es /p/v5/578.html   (275 words)

 Polygon - Uncyclopedia, the content-free encyclopedia In geometry, a polygon is a shape, or a digital photograph of a shape, which is composed of one or more individual gons. The first known polygon, the semi-irregular truncated heptadecagon, was discovered by Isosceles of Crete in 1492 BCE (17 years after he made the startling discovery that both of his legs were of the same length). Within the next few minutes, billions and billions of polygons were classified, catalogued, and wikified by Ancient Greece's vast army of philosophers, mathematicians, sages, orators, poets, pundits, and other thinking persons that for the moment had nothing better to do on a Saturday night (other than opportunistic wanking). uncyclopedia.org /wiki/Polygon   (417 words)

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