Degenerate
A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. Forexample, the Point is a degenerate case of the Circle as the Radius approaches 0, and theCircle is a degenerate form of an Ellipse as the Eccentricity approaches 0. Another example is the twoidentical Roots of the second-order Polynomial 
. Since the 
Roots of an th degreePolynomial are usually distinct, Roots which coincide are said to be degenerate. Degenerate cases often requirespecial treatment in numerical and analytical solutions. For example, a simple search for both Roots of the aboveequation would find only a single one: 1.
The word degenerate also has several very specific and technical meanings in different branches of mathematics.
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 513-514, 1985.
- Small Dodecicosacron
- Small Dodecicosahedron
- Small Dodecicosidodecahedron
- Small Hexacronic Icositetrahedron
- Small Hexagonal Hexecontahedron
- Small Hexagrammic Hexecontahedron
- Small Icosacronic Hexecontahedron
- Small Icosicosidodecahedron
- Small Icosihemidodecacron
- Small Icosihemidodecahedron
- Small Inverted Retrosnub Icosicosidodecahedron
- Axial Vector
- Axiom
- Axiom A Diffeomorphism
- Axiom A Flow
- Axiomatic Set Theory
- Axiomatic System
- Axiom of Choice
- Axis
- Ax-Kochen Isomorphism Theorem
- B2-Sequence
- Baby Monster Group
- BAC-CAB Identity
- BAC-CAB Rule
- Bachelier Function