# Closed (Geometry)

Pronunciation: /kloʊzd/ Explain

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

 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.

 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. McAdams, David E.. All Math Words Dictionary, closed. 2nd Classroom edition 20150108-4799968. pg 34. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. closed. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/closed. Buy the book

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

McAdams, David E. Closed (Geometry). 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/closed_g.html.

### Revision History

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