Convex polygon: Difference between revisions
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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. | 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 [[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 == | == See also == | ||
Revision as of 08:12, 22 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.
The area of a regular n-gon of side length s is 
See also
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