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. |
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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. | ||
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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]]. | ||
| − | + | 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
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