Degenerate

Pronunciation: /dɪˈdʒɛn.ə.rɪt/ Explain

A degenerate case is a case where the class of an object changes to a usually simpler object. Degenerate cases are limiting, meaning that the original object can not be changed any further. Table 1 shows a number of degenerate objects.

General case	Degenerate case
Circle	A circle with a radius of zero has degenerated to a point.
Rectangle	A rectangle with one side having a length of zero has degenerated to a line segment.
Hyperbola	A hyperbola can degenerate into two lines crossing at a point.
Continuum	A degenerate continuum is a single point.
Table 1: Degenerate objects

References

1. McAdams, David E.. All Math Words Dictionary, degenerate. 2nd Classroom edition 20150108-4799968. pg 56. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Degenerate. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/degenerate.html.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/22/2010: Added "References". (McAdams, David E.)
12/4/2008: Initial version. (McAdams, David E.)