# Difference between revisions of "Convex polygon"

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− | + | [[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. |

+ | |||

+ | All [[internal angle]]s of a convex polygon are less than <math>180^{\circ}</math>. These internal angles sum to <math>180(n-2)</math> degrees. | ||

+ | |||

+ | The [[convex hull]] of a set of points also turns out to be the convex polygon with some or all of the points as its [[vertices]]. | ||

− | + | The area of a regular [[n-gon]] of side [[length]] s is <math>\frac{ns^2*\tan{(90-\frac{180}{n})}}{4}</math> | |

− | {{ | ||

+ | == See also == | ||

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

+ | * [[Convex polyhedron]] | ||

+ | {{stub}} | ||

[[Category:Definition]] | [[Category:Definition]] |

## Revision as of 12:03, 27 September 2007

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.

All internal angles of a convex polygon are less than . These internal angles sum to degrees.

The convex hull of a set of points also turns out to be the convex polygon with some or all of the points as its vertices.

The area of a regular n-gon of side length s is

## See also

*This article is a stub. Help us out by expanding it.*