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.
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.
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. McAdams, David E.. All Math Words Dictionary, open. 2nd Classroom edition 20150108-4799968. pg 130. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

• McAdams, David E.. Closed (Geometry). allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 9/6/2018. https://www.allmathwords.org/en/c/closed_g.html.

Cite this article as:

McAdams, David E. Open (Geometry). 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/o/open_g.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

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/5/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
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.)