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 caseDegenerate case
CircleA circle with a radius of zero has degenerated to a point.
RectangleA rectangle with one side having a length of zero has degenerated to a line segment.
HyperbolaA hyperbola can degenerate into two lines crossing at a point.
ContinuumA degenerate continuum is a single point.
Table 1: Degenerate objects


  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.

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.)

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