Connected

Pronunciation: /kəˈnɛk.tɪd/ Explain

A geometric figure is connected if it is all in one piece. The mathematically exact definition of connected is:

Definition: A geometric figure is connected if and only if, for any two points in the figure, a path exists between the points that does not leave the figure. If a figure is not connected, it is disconnected.

Figure 1: 8 is a connected figure

Consider a figure 8. One can select any point and follow a path to any other point, even on the other side of the 8. A figure 8 is a connected geometric figure. Now consider the letter 'i' as a geometric figure. Select a point on the dot above the i. There is no path to the main part of the i that does not leave the dot. The letter 'i' is a disconnected figure.

Figure 2: i is a disconnected figure

References

1. McAdams, David E.. All Math Words Dictionary, connected. 2nd Classroom edition 20150108-4799968. pg 43. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Connected. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/connected.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.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)