Difference between revisions of "Convex polygon"

m (typo fix)
Line 7: Line 7:
 
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
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

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS