Difference between revisions of "Convex polygon"

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[[Image:convex_polygon.png|right]]
  
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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.
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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]].
  
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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The area of a regular [[n-gon]] of side [[length]] s is <math>\frac{ns^2*\tan{(90-\frac{180}{n})}}{4}</math>
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== See also ==
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* [[Concave polygon]]
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* [[Convex polyhedron]]
  
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[[Category:Definition]]

Revision as of 12:03, 27 September 2007

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.

The area of a regular n-gon of side length s is $\frac{ns^2*\tan{(90-\frac{180}{n})}}{4}$

See also

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