Closed (Geometry)

Pronunciation: /kloʊzd/ Explain

A geometric figure is closed if the entire boundary of the figure is part of the figure.[1]

Open geometric figure
Figure 1: An open geometric figure

The clearest example of this is a graph of inequalities. Figure 1 is the graph of a system of inequalities. The points on the line y < 3 - x is part of the boundary. However, since the inequality y < 3 - x does not include the points on the line, the shaded geometric figure is not closed.

Closed geometric figure
Figure 2: A closed geometric figure

In figure 2, the inequality y <= 3 - x does include the points on the line, so the shaded geometric figure is closed.

References

  1. closed. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/closed.

More Information

  • McAdams, David E.. Open. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/g/g_open.html.

Cite this article as:

McAdams, David E. Closed (Geometry). 6/29/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/closed_g.html.

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Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
8/2/2008: Added dictionary.com to More Information (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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