What does a polygon have

What Is a Polygon?

What does a polygon have

what does a polygon have

Types of Polygon Shape Names with Sides and Pictures

May 17,  · Definition of a Polygon A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all . Nov 15,  · A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. The line segments of a polygon are called sides or edges. The point where two line segments meet is called vertex or corners, henceforth an angle is formed.

For longer bridges the funicular polygon affords a method of determining maximum bending moments which is perhaps more convenient. The regiment had evacuated Polygon Wood on the night of the third. It is the most northern part of How long does it take to get a provisional license America, in shape like a polygonwith the southern side the longest.

The term polygon is applied to figures having flat sides equidistant from a common centre. In geometrya closed figure having three or more sides and lying on one plane. New Word List Word List. Save This Word! See synonyms for polygon on Thesaurus. Set some time apart to test your bracket symbol knowledge, and see if you can keep your parentheses, squares, curlies, and angles all straight! See poly--gon. Words nearby polygon polygenismpolyglandularpolyglandular deficiency syndromepolyglotPolygnotuspolygonpolygonaceouspolygonumpolygraphpolygynistpolygynous.

Words related to polygon shapeformdodecagonoctagondecagonpentagontrianglequadranglehexagonquadrilateralparallelogramtrapezoid. Example sentences from the Web for polygon For longer bridges the funicular polygon affords a method of determining maximum bending moments which is perhaps more convenient. Guatemala, the country of the future Charles M. A regular polygon has all its sides and angles equal. Specific polygons are named according to the number of sides, such as triangle, pentagon, etc.

A what does a polygon have plane figure having three or more sides. Triangles, rectangles, and octagons are all examples of polygons. All rights reserved. Tired of Typos? Get Help Now!

What is a Regular Polygon?

Polygon Definition A polygon is a plane figure that closes in a space using only line segments. If it must use only line segments and must close in a space, the polygon with the fewest sides has to be the triangle (three sides and interior angles). a closed plane figure bounded by three or more straight sides that meet in pairs in the same number of vertices, and do not intersect other than at these vertices. The sum of the interior angles is (n –2) ? ° for n sides; the sum of the exterior angles is °. A regular polygon has . 66 rows · Aug 10,  · Polygons are 2D shapes that have a certain number of sides. Their sides .

The solid plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit 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 a solid polygon is sometimes called its body.

An n -gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly.

A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. There are many more generalizations of polygons defined for different purposes. Polygons are primarily classified by the number of sides. See the table below. Euclidean geometry is assumed throughout.

Any polygon has as many corners as it has sides. Each corner has several angles. The two most important ones are:. If the polygon is non-self-intersecting that is, simple , the signed area is. The signed area depends on the ordering of the vertices and of the orientation of the plane. Commonly, the positive orientation is defined by the counterclockwise rotation that maps the positive x -axis to the positive y -axis. If the vertices are ordered counterclockwise that is, according to positive orientation , the signed area is positive; otherwise, it is negative.

In either case, the area formula is correct in absolute value. This is commonly called the shoelace formula or Surveyor's formula.

The area A of a simple polygon can also be computed if the lengths of the sides, a 1 , a 2 , The formula was described by Lopshits in If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points: the former number plus one-half the latter number, minus 1.

For any two simple polygons of equal area, the Bolyai—Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon.

The lengths of the sides of a polygon do not in general determine its area. Of all n -gons with a given perimeter, the one with the largest area is regular and therefore cyclic. Many specialized formulas apply to the areas of regular polygons. The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by. This radius is also termed its apothem and is often represented as a.

The area of a regular n -gon in terms of the radius R of its circumscribed circle can be expressed trigonometrically as: [11] [12]. The area of a self-intersecting polygon can be defined in two different ways, giving different answers:.

Using the same convention for vertex coordinates as in the previous section, the coordinates of the centroid of a solid simple polygon are. The centroid of the vertex set of a polygon with n vertices has the coordinates. Individual polygons are named and sometimes classified according to the number of sides, combining a Greek -derived numerical prefix with the suffix -gon , e.

The triangle , quadrilateral and nonagon are exceptions. Beyond decagons sided and dodecagons sided , mathematicians generally use numerical notation, for example gon and gon. Exceptions exist for side counts that are more easily expressed in verbal form e. Some special polygons also have their own names; for example the regular star pentagon is also known as the pentagram.

To construct the name of a polygon with more than 20 and less than edges, combine the prefixes as follows. Conway for clarity to concatenated prefix numbers in the naming of quasiregular polyhedra.

Polygons have been known since ancient times. The regular polygons were known to the ancient Greeks, with the pentagram , a non-convex regular polygon star polygon , appearing as early as the 7th century B. The first known systematic study of non-convex polygons in general was made by Thomas Bradwardine in the 14th century. In , Geoffrey Colin Shephard generalized the idea of polygons to the complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons.

Polygons appear in rock formations, most commonly as the flat facets of crystals , where the angles between the sides depend on the type of mineral from which the crystal is made.

Regular hexagons can occur when the cooling of lava forms areas of tightly packed columns of basalt , which may be seen at the Giant's Causeway in Northern Ireland , or at the Devil's Postpile in California. In biology , the surface of the wax honeycomb made by bees is an array of hexagons , and the sides and base of each cell are also polygons.

In computer graphics , a polygon is a primitive used in modelling and rendering. They are defined in a database, containing arrays of vertices the coordinates of the geometrical vertices , as well as other attributes of the polygon, such as color, shading and texture , connectivity information, and materials. Any surface is modelled as a tessellation called polygon mesh. Where n is large, this approaches one half. Or, each vertex inside the square mesh connects four edges lines.

The imaging system calls up the structure of polygons needed for the scene to be created from the database. This is transferred to active memory and finally, to the display system screen, TV monitors etc. During this process, the imaging system renders polygons in correct perspective ready for transmission of the processed data to the display system. Although polygons are two-dimensional, through the system computer they are placed in a visual scene in the correct three-dimensional orientation.

This is called the point in polygon test. From Wikipedia, the free encyclopedia. Plane figure bounded by line segments. For other uses, see Polygon disambiguation. Main article: Polygon computer graphics. This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. October Learn how and when to remove this template message. A new universal etymological technological, and pronouncing dictionary of the English language.

Oxford University. Extract of p. Beyond measure: a guided tour through nature, myth, and number. World Scientific. ISBN Nagy, L. Retrieved 6 Feb The College Mathematics Journal. JSTOR Archived from the original PDF on Lopshits Computation of areas of oriented figures. Advances in Applied Mathematics. MR S2CID Honsberger, editor. Learning and Teaching Mathematics. Aronov et al.

The Computer Graphics Manual. Ask Dr. The Math Forum — Drexel University. Retrieved 3 May Historia Mathematica. Archived from the original PDF on 12 May Retrieved 18 April Geometry demystified Online-Ausg. New York: McGraw-Hill. Jack, Philosophy and Journalism , Longman, , p. Reprint of original publication with corrected errata. Heath uses the Latinized spelling "Aristophonus" for the vase painter's name.

London Math. In Halperin, Dan; Mehlhorn, Kurt eds.

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