Degeneracy
Degeneracy
Often, the degenerate cases are the exceptional circumstances where changes to the same old dimension or the cardinality of the object happen. For instance, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, which makes its dimension one. This is much like the case of a circle, whose dimension shrinks from two to zero because it degenerates into a degree. In such a degenerate case, the answer set is said to be degenerate.
- Some common synonyms of degenerate are corrupt, iniquitous, nefarious, vicious, and villainous.
- The definitions of many classes of composite or structured objects usually implicitly embrace inequalities.
- For example, the angles and the side lengths of a triangle are imagined to be constructive.
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- In the case of triangles, one has a degenerate triangle if at least one facet size or angle is zero (equiv., it turns into a “line segment”).
A degenerate case thus has particular options which makes it non-generic. For example, proper triangles, isosceles triangles and equilateral triangles are non-generic and non-degenerate. In fact, degenerate cases usually correspond to singularities, either within the object or in some configuration area. For instance, a conic section is degenerate if and provided that it has singular points (e.g., level, line, intersecting traces).
Study Extra About Degenerate
In contexts where self-intersection is allowed, a sphere is a degenerate commonplace torus where the axis of revolution passes via the middle of the generating circle, somewhat than outside it. A convex polyhedron is degenerate if either two adjoining sides are coplanar or two edges are aligned. In the case of a tetrahedron, that is equal to saying that each one of its vertices lie in the same aircraft, giving it a volume of zero. A degenerate triangle has collinear vertices and 0 space, and thus coincides with a section covered twice (if the three vertices usually are not all equal; otherwise, the triangle degenerates to a single level).
We’ve arranged the synonyms in size order in order that they’re simpler to seek out. For some lessons of composite objects, the degenerate instances depend upon the properties that are specifically studied. In particular, the category of objects may often be defined or characterized by systems of equations. This could be the purpose for which there isn’t any general definition of degeneracy, despite the fact that the concept is broadly used and defined in each particular state of affairs.