﻿ Closed (Geometry): A geometric figure is closed if the entire boundary of the figure is part of the figure.

# Closed (Geometry)

Pronunciation: /kloʊzd/ ?

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. closed. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-04). http://www.merriam-webster.com/dictionary/closed.

• McAdams, David. Open. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem.org. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Open%20(Geometry).
• McAdams, David. Closed (sets). allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem.org. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Closed%20(sets).

Closed (Geometry). 2010-01-04. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/g/g_closed.html.