If the three vertices are pairwise distinct, it has two 0° angles and one a hundred and eighty° angle. If two vertices are equal, it has one 0° angle and two undefined angles. A hyperbola can degenerate into two traces crossing at a degree, by way of a household of hyperbolae having those lines as frequent asymptotes.

- In the case of a tetrahedron, this is equal to saying that every one of its vertices lie in the same airplane, giving it a quantity of zero.
- If two vertices are equal, it has one zero° angle and two undefined angles.
- This may be the reason for which there isn’t a general definition of degeneracy, despite the fact that the concept is broadly used and defined in every particular situation.
- A degenerate conic is a conic section (a second-degree airplane curve, defined by a polynomial equation of diploma two) that fails to be an irreducible curve.
- Specifically, nefarious suggests flagrant breaching of time-honored laws and traditions of conduct.

an individual who has declined, as in morals or character, from a kind or commonplace thought of regular. Relationships of frequencies of codons for various amino acids in the genetic code and the observed frequencies of amino acids in proteins of living methods (drawn from Lewin’s»Genes IV»). If you check with the behaviour of a group of individuals as degeneracy, you imply that you just suppose it is stunning, immoral, or disgusting. The definition of an improvement is an increase in worth, situation or quality. The meanings of villainous and degenerate largely overlap; nevertheless, villainous applies to any evil, depraved, or vile conduct or attribute.

## Oxford English And Spanish Dictionary, Synonyms, And Spanish To English Translator

In contexts where self-intersection is allowed, a sphere is a degenerate commonplace torus where the axis of revolution passes by way of the center of the producing circle, rather than exterior it. A convex polyhedron is degenerate if either two adjacent aspects are coplanar or two edges are aligned. In the case of a tetrahedron, that is equivalent to saying that every one of its vertices lie in the identical aircraft, giving it a quantity of zero. A degenerate triangle has collinear vertices and nil space, and thus coincides with a segment covered twice (if the three vertices aren’t all equal; in any other case, the triangle degenerates to a single point).

A circle could be considered a degenerate ellipse, because the eccentricity approaches 0. A line segment can be viewed as a degenerate case of an ellipse by which the semiminor axis goes to zero, the foci go to the endpoints, and the eccentricity goes to at least one. The line is a degenerate case of a parabola if the parabola resides on a tangent aircraft. In inversive geometry, a line is a degenerate case of a circle, with infinite radius. A degenerate conic is a conic part (a second-degree plane curve, outlined by a polynomial equation of degree two) that fails to be an irreducible curve.

### Synonyms & Antonyms Of Degenerate

DisclaimerAll content on this website, together with dictionary, thesaurus, literature, geography, and different reference data is for informational purposes only. This data shouldn’t be thought of full, updated, and isn’t supposed for use instead of a visit, consultation, or advice of a authorized, medical, or some other skilled. In some conditions, the phrases vicious and degenerate are roughly equivalent. However, vicious may directly oppose virtuous in implying moral depravity, or could connote malignancy, cruelty, or destructive violence.

In quantum mechanics, any such multiplicity in the eigenvalues of the Hamiltonian operator provides rise to degenerate energy ranges. Usually any such degeneracy signifies some underlying symmetry in the system. A convex polygon is degenerate if at least two consecutive sides coincide at least partially, or no less than one facet has zero size, or a minimum of one angle is 180°. Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides. In the case of triangles, this definition coincides with the one which has been given above. In arithmetic, a degenerate case is a limiting case of a class of objects which seems to be qualitatively different from the rest of the category, and the time period degeneracy is the situation of being a degenerate case.

The morale of the troopers degenerated, and they were unable to struggle. The synonyms iniquitous and degenerate are sometimes interchangeable, but iniquitous implies absence of all signs of justice or equity. good, wholesome, strong, noble, kind, virtuous, good, enhance, honorable, rise, uncorrupted, properly, aid, grow, recuperate, pure, incorruptible, assist, develop, upright, enhance, build, ethical, Uncorrupt, clean, honest, progress. The synonyms have been organized relying on the number of charachters so that they’re simple to seek out. A random variable which can solely take one worth has a degenerate distribution; if that worth is the true quantity 0, then its probability density is the Dirac delta perform. When the radius of a sphere goes to zero, the resulting degenerate sphere of zero quantity is a degree.