Open (Geometry)

Pronunciation: /ˈoʊ pən/ Explain

A geometric figure is open if any part of the boundary of the figure is not part of the figure.

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 are not part of the boundary. Since the inequality y < 3 - x does not include the points on the line, the shaded geometric figure is open.

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 not open.

References

  1. open. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 3/12/2009. http://www.merriam-webster.com/dictionary/open.

More Information

  • McAdams, David E. Closed (sets). allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/c/closed.html.

Cite this article as:

McAdams, David E. Open (Geometry). 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/open_g.html.

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Revision History

10/2/2010: Clarified definition. (McAdams, David E.)
8/2/2008: Added dictionary.com to More Information (McAdams, David E.)
6/11/2008: Added hot link for inequality. (McAdams, David E.)
7/30/2007: Initial version. (McAdams, David E.)

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