Polygon: Difference between revisions
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A '''polygon''' is a two-[[dimension]]al [[geometry|geometric]] closed figure bounded by a continuous set of [[line segments]]. A polygon, in [[Euclidian geometry]], must have at least three sides. A polygon of three sides is called a [[triangle]], four sides a [[quadrilateral]], five sides a [[pentagon]], six sides a [[hexagon]]. Figures with more sides are typically named with the Greek name for the number of sides, followed by "-gon". Mathematicians discussing the properties of polygons with large numbers of sides will often use the formulation '''''n''-gon''', where ''n'' is replaced by the number of sides (ie, a 17-gon or a 100-gon). When discussing the properties of classes of polygons which include polygons of different numbers of sides, mathematicians will sometimes refer to '''''n''-gon''', without substituting the ''n''. | A '''polygon''' is a two-[[dimension]]al [[geometry|geometric]] closed figure bounded by a continuous set of [[line segments]]. A polygon, in [[Euclidian geometry]], must have at least three sides. A polygon of three sides is called a [[triangle]], four sides a [[quadrilateral]], five sides a [[pentagon]], six sides a [[hexagon]]. Figures with more sides are typically named with the Greek name for the number of sides, followed by "-gon". Mathematicians discussing the properties of polygons with large numbers of sides will often use the formulation '''''n''-gon''', where ''n'' is replaced by the number of sides (ie, a 17-gon or a 100-gon). When discussing the properties of classes of polygons which include polygons of different numbers of sides, mathematicians will sometimes refer to '''''n''-gon''', without substituting the ''n''. | ||
The line segments bounding a polygon are known as '''sides''', and the points where the sides meet are '''vertices''' (singular '''vertex'''). | The line segments bounding a polygon are known as '''sides''', and the [[point (geometry)|points]] where the sides meet are '''vertices''' (singular '''vertex'''). | ||
A polygon is known as a [[simple polygon]] if none of its sides cross other sides, and each vertex is the meeting point of only two sides. A polygon which does not meet this criterion is a [[complex polygon]]. A polygon is called [[convex]] when there are no line segments which connect two points within the polygon which pass outside the polygon. Convex polygons have no internal angles between two adjacent sides greater than 180 [[degrees of arc]]. A polygon which has all sides of equal length is known as an '''equilateral polygon'''. A convex polygon which has all sides and all internal angles equal is known as a '''regular polygon'''. A complex polygon which has all sides and all angles equal is known as a '''regular star polygon'''. | A polygon is known as a [[simple polygon]] if none of its sides cross other sides, and each vertex is the meeting point of only two sides. A polygon which does not meet this criterion is a [[complex polygon]]. A polygon is called [[convex]] when there are no line segments which connect two points within the polygon which pass outside the polygon. Convex polygons have no internal angles between two adjacent sides greater than 180 [[degrees of arc]]. A polygon which has all sides of equal length is known as an '''equilateral polygon'''. A convex polygon which has all sides and all internal angles equal is known as a '''regular polygon'''. A complex polygon which has all sides and all angles equal is known as a '''regular star polygon'''. | ||
Revision as of 13:08, 22 April 2007
A polygon is a two-dimensional geometric closed figure bounded by a continuous set of line segments. A polygon, in Euclidian geometry, must have at least three sides. A polygon of three sides is called a triangle, four sides a quadrilateral, five sides a pentagon, six sides a hexagon. Figures with more sides are typically named with the Greek name for the number of sides, followed by "-gon". Mathematicians discussing the properties of polygons with large numbers of sides will often use the formulation n-gon, where n is replaced by the number of sides (ie, a 17-gon or a 100-gon). When discussing the properties of classes of polygons which include polygons of different numbers of sides, mathematicians will sometimes refer to n-gon, without substituting the n.
The line segments bounding a polygon are known as sides, and the points where the sides meet are vertices (singular vertex).
A polygon is known as a simple polygon if none of its sides cross other sides, and each vertex is the meeting point of only two sides. A polygon which does not meet this criterion is a complex polygon. A polygon is called convex when there are no line segments which connect two points within the polygon which pass outside the polygon. Convex polygons have no internal angles between two adjacent sides greater than 180 degrees of arc. A polygon which has all sides of equal length is known as an equilateral polygon. A convex polygon which has all sides and all internal angles equal is known as a regular polygon. A complex polygon which has all sides and all angles equal is known as a regular star polygon.