# Difference between revisions of "Convex polygon"

m (A little typo on the sum of the exterior angles. It should be 360 not 360n) |
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[[Image:convex_polygon.png|right]] | [[Image:convex_polygon.png|right]] | ||

− | A '''convex polygon''' is a [[polygon]] whose [[interior]] forms a [[convex set]]. That is, if any 2 points on the [[perimeter]] of the polygon are connected by a [[line segment]], no point on that segment will be outside the polygon. | + | A '''convex polygon''' is a [[polygon]] whose [[interior]] forms a [[convex set]]. That is, if any 2 points on the [[perimeter]] of the polygon are connected by a [[line segment]], no point on that segment will be outside the polygon. For example, every [[regular polygon]] is convex. |

− | All [[internal angle]]s of a convex polygon are less than <math>180^{\circ}</math>. | + | All [[internal angle]]s of a convex polygon are less than <math>180^{\circ}</math>. Equivalently, all [[external angle]]s are less than <math>180^{\circ}</math>. The sum of the exterior angles of any convex polygon is <math>360^\circ</math> and the sum of the internal angles of a convex <math>n</math>-gon is <math>(n - 2)180^\circ</math>. |

− | The [[convex hull]] of a set of points | + | The [[convex hull]] of a [[finite]] set of points is a convex polygon with some or all of the points as its [[vertex | vertices]]. |

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== See also == | == See also == | ||

* [[Concave polygon]] | * [[Concave polygon]] |

## Revision as of 21:53, 1 March 2008

A **convex polygon** is a polygon whose interior forms a convex set. That is, if any 2 points on the perimeter of the polygon are connected by a line segment, no point on that segment will be outside the polygon. For example, every regular polygon is convex.

All internal angles of a convex polygon are less than . Equivalently, all external angles are less than . The sum of the exterior angles of any convex polygon is and the sum of the internal angles of a convex -gon is .

The convex hull of a finite set of points is a convex polygon with some or all of the points as its vertices.

## See also

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