Convex Polygon

Pronunciation: /kɒnˈvɛks ˈpɒl iˌgɒn/ Explain

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.

Click on the blue points and drag them to change the figure.

If an angle at a vertex is a straight line, and all the other angles are less than 180 degrees, is the polygon concave or convex?
Manipulative 1 - Concave Polygon Created with GeoGebra.

References

  1. convex polygon. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. http://www.merriam-webster.com/dictionary/convex polygon.
  2. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry. pg 54. www.archive.org. Ginn & Company. 1899. Last Accessed 8/6/2018. http://www.archive.org/stream/newplaneandsoli02smitgoog#page/n69/mode/1up/search/convex. Buy the book
  3. Lyman, Elmer A.. Plane and Solid Geometry. pg 57. www.archive.org. American Book Company. 1908. Last Accessed 8/6/2018. http://www.archive.org/stream/planesolidgeomet00lymarich#page/57/mode/1up/search/convex. Buy the book

Cite this article as:

McAdams, David E. Convex Polygon. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/convexpolygon.html.

Image Credits

Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/18/2010: Added "References". (McAdams, David E.)
7/30/2007: Initial version. (McAdams, David E.)

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