Difference between revisions of "Convex polygon"
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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. | ||
| − | 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>. These internal angles sum to <math>180(n-2)</math> degrees. |
| − | These internal angles sum to 180(n-2) degrees. | ||
| − | The [[ | + | 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. |
== See also == | == See also == | ||
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* [[Convex polyhedron]] | * [[Convex polyhedron]] | ||
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[[Category:Definition]] | [[Category:Definition]] | ||
Revision as of 18:42, 21 September 2007
| This is an AoPSWiki Word of the Week for Sep 20-26 |
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.
See also
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