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.  For example, every [[regular polygon]] is convex.
 
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.  For example, every [[regular polygon]] is convex.
  
All [[internal angle]]s of a convex polygon are less than <math>180^{\circ}</math>.  Equivalently, all [[external angle]]s are less than <math>180^{\circ}</math>.  The sum of the exterior angles of any convex polygon is <math>360^\circ</math> and the sum of the internal angles of a convex <math>n</math>-gon is <math>(n - 2)180^\circ</math>.
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All [[interior angle|interior angles]] of a convex polygon are less than <math>180^{\circ}</math>.  Equivalently, all [[exterior angle|exterior angles]] are less than <math>180^{\circ}</math>.  The sum of the exterior angles of any convex polygon is <math>360^\circ</math> and the sum of the internal angles of a convex <math>n</math>-gon is <math>(n - 2)180^\circ</math>.
  
 
The [[convex hull]] of a [[finite]] set of points is a convex polygon with some or all of the points as its [[vertex | vertices]].
 
The [[convex hull]] of a [[finite]] set of points is a convex polygon with some or all of the points as its [[vertex | vertices]].

Latest revision as of 21:10, 27 February 2020

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. For example, every regular polygon is convex.

All interior angles of a convex polygon are less than $180^{\circ}$. Equivalently, all exterior angles are less than $180^{\circ}$. The sum of the exterior angles of any convex polygon is $360^\circ$ and the sum of the internal angles of a convex $n$-gon is $(n - 2)180^\circ$.

The convex hull of a finite set of points is a convex polygon with some or all of the points as its vertices.

See also

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