Write down the name of the simplest polygon.
Answers
Answer:
{{short description|flat shape consisting of straight, non-intersecting lines}}
{{Refimprove|date=October 2009}}
[[File:Polygons Examples of polygons.png|thumb|Some simple polygons.]]
In [[geometry]], a '''simple polygon''' {{IPAc-en|ˈ|p|ɒ|l|ɪ|ɡ|ɒ|n}} is a [[polygon]] that does not [[Intersection (Euclidean geometry)|intersect]] itself and has no holes. That is, it is a flat shape consisting of straight, non-intersecting [[line segment]]s or "sides" that are joined pairwise to form a single [[closed curve|closed]] path. If the sides intersect then the polygon is not simple. The qualifier "simple" is frequently omitted, with the above definition then being understood to define a polygon in general.
The definition given above ensures the following properties:
* A polygon encloses a region (called its interior) which always has a measurable [[area]].
* The line segments that make up a polygon (called sides or edges) meet only at their endpoints, called vertices (singular: vertex) or less formally "corners".
* Exactly two edges meet at each vertex.
* The number of edges always equals the number of vertices.
Two edges meeting at a corner are usually required to form an [[angle]] that is not straight (180°); otherwise, the [[collinear]] line segments will be considered parts of a single side.
Mathematicians typically use "polygon" to refer only to the shape made up by the line segments, not the enclosed region, however some may use "polygon" to refer to a [[plane (mathematics)|plane]] [[Shape|figure]] that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e., by a [[closed polygonal chain]]). According to the definition in use, this boundary may or may not form part of the polygon itself.<ref>Grünbaum, B.; ''[[Convex Polytopes]]'' 2nd Ed, Springer, 2003</ref>
Simple polygons are also called '''Jordan polygons''', because the [[Jordan curve theorem]] can be used to prove that such a polygon divides the plane into two regions, the region inside it and the region outside it. A polygon in the plane is simple if and only if it is [[Homeomorphism|topologically equivalent]] to a [[circle]]. Its interior is topologically equivalent to a [[disk (mathematics)|disk]].
Answer:
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