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Convex and concave polygons

regular]] pentagon In geometry, a polygon can be either convex or concave (non-convex or reentrant).

Contents


Convex polygons

A convex polygon is a simple polygon whose interior is a convex set.[1] The following properties of a simple polygon are all equivalent to convexity:

  • Every internal angle is less than or equal to 180 degrees.
  • Every line segment between two vertices remains inside or on the boundary of the polygon.

A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two nonadjacent vertices of the polygon is strictly interior to the polygon except at its endpoints.

Every nondegenerate triangle is strictly convex.

Concave or non-convex polygons

An example of a concave polygon. A simple polygon that is not convex is called concave,[2] non-convex[3] or reentrant.[4] A concave polygon will always have an interior angle with a measure that is greater than 180 degrees.[5]

It is always possible to partition a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex polygons as possible is described by .[6]

See also

  • Convex hull
  • Cyclic polygon
  • Tangential polygon

References

  1. Definition and properties of convex polygons with interactive animation.
  2. .
  3. .
  4. Definition and properties of concave polygons with interactive animation.
  5. .

External links

ar: bs:Konveksni poligon ca:Pol gons convexs i c ncaus et:Kumer hulknurk es:Pol gono convexo eo:Konveksa plurlatero eu:Poligono ganbil he: ru: sl:Konveksni in konkavni mnogokotnik fi:Konveksi monikulmio th:






Source: Wikipedia | The above article is available under the GNU FDL. | Edit this article



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