# 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.

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

• 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.

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.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)