Concave Polygon

Pronunciation: /ˈkɒn keɪv ˈpɒ liˌgɒn/ ?
concave polygon
Figure 1: Concave Polygon

Figure 1 is an example of a concave polygon. Note that part of the line between the two points in the figure lie outside the polygon.

convex polygon
Figure 2: Convex 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.

A polygon is a closed shape whose boundaries consist of straight lines. A polygon is concave if, for any two points that are part of the shape, a straight line can be drawn between the two points that lies outside the shape.[1] A property of concave polygons is that if the sides are extended, the extension of at least two sides will intersect one of the other sides.

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Manipulative 1: Concave and convex polygons. Click on the blue points and drag them to change the figure. Created with GeoGebra

References

  1. concave polygon. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-05). http://www.merriam-webster.com/dictionary/concave 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/concave.
  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/56/mode/2up/search/concave.

Cite this article as:


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

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Revision History


2010-01-19: Corrected description of figure 1, added manipulative 1 (McAdams, David.)
2010-01-18: Added "References" (McAdams, David.)
2007-07-30: Initial version (McAdams, David.)

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