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>.  
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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 [[comvex hull]] of a set of points also turns out to be the convex polygon with some or all of the points as its vertices.
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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
Convex polygon.png

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 $180^{\circ}$. These internal angles sum to $180(n-2)$ 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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