Convex Polygon

Pronunciation: /kɒnˈvɛks ˈpɒl iˌgɒn/ ?

A polygon is a closed shape whose boundaries consist of straight lines. A shape if convex if, for any two points that are part of the shape, a straight line can not be drawn between the two points that lies outside the shape.[1]

convex polygon
Figure 1: Convex polygon

Figure 1 is an example of a concave polygon. Since it is possible to pick two points within the shape and draw a line between them that leaves the shape, the shape is convex.

concave polygon
Figure 2: Concave Polygon

Figure 2 is an example of a convex polygon. Note that the entire line is contained within the polygon. In fact, a line drawn between any two points that are part of the' polygon will be entirely contained within the polygon.

References

  1. convex polygon. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-05). http://www.merriam-webster.com/dictionary/convex polygon.
  2. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry, pg 54. Ginn & Company, 1899. (Accessed: 2010-01-18). http://www.archive.org/stream/newplaneandsoli02smitgoog#page/n69/mode/1up/search/convex.
  3. Lyman, Elmer A.. Plane and Solid Geometry, pg 57. American Book Company, 1908. (Accessed: 2010-01-18). http://www.archive.org/stream/planesolidgeomet00lymarich#page/57/mode/1up/search/convex.

Cite this article as:


Convex Polygon. 2010-01-18. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/convexpolygon.html.

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2010-01-18: Added "References" (McAdams, David.)
2007-07-30: Initial version (McAdams, David.)

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