Concave Polygon

Pronunciation: /ˈkɒn.keɪv ˈpɒ.liˌgɒn/ Explain

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. 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. Also, a polygon is concave if any of the interior angles is greater than 180°.

References

1. McAdams, David E.. All Math Words Dictionary, concave. 2nd Classroom edition 20150108-4799968. pg 41. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. concave polygon. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/concave polygon. Buy the book
3. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry. pg 54. www.archive.org. Ginn & Company. 1899. Last Accessed 6/25/2018. http://www.archive.org/stream/newplaneandsoli02smitgoog#page/n69/mode/1up/search/concave. Buy the book
4. Lyman, Elmer A.. Plane and Solid Geometry. pg 57. www.archive.org. American Book Company. 1908. Last Accessed 6/25/2018. http://www.archive.org/stream/planesolidgeomet00lymarich#page/56/mode/2up/search/concave. Buy the book

Cite this article as:

McAdams, David E. Concave Polygon. 3/9/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/concavepolygon.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

3/9/2019: Removed faulty manipulative. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/19/2010: Corrected description of figure 1, added manipulative 1. (McAdams, David E.)
1/18/2010: Added "References". (McAdams, David E.)
7/30/2007: Initial version. (McAdams, David E.)