Pronunciation: /dɪˈdʒɛn ə rɪt/ ?

A degenerate case is a case where the class of an object changes to a usually simpler object.[1] 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 is a point.
RectangleA rectangle with one side having a length of zero is 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. degenerate. WordNet. Princeton University. (Accessed: 2011-01-08).

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Degenerate. 2010-01-22. All Math Words Encyclopedia. Life is a Story Problem LLC.


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2010-01-22: Added "References" (McAdams, David.)
2008-12-04: Initial version (McAdams, David.)

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