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hyperbolic    音标拼音: [h,ɑɪpɚb'ɑlɪk]
a. 双曲线的;夸张的

双曲线的;夸张的

hyperbolic
双曲线 HYP

hyperbolic
双曲线 双曲

hyperbolic
adj 1: enlarged beyond truth or reasonableness; "a hyperbolic
style" [synonym: {hyperbolic}, {inflated}]
2: of or relating to a hyperbola; "hyperbolic functions"

Hyperbolic \Hy`per*bol"ic\, Hyperbolical \Hy`per*bol"ic*al\, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
[1913 Webster]

2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression. "This
hyperbolical epitaph." --Fuller.
[1913 Webster]

{Hyperbolic functions} (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called {hyperbolic sines}, {hyperbolic cosines},
etc.

{Hyperbolic logarithm}. See {Logarithm}.

{Hyperbolic spiral} (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector.
[1913 Webster]


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  • Why are certain PDE called elliptic, hyperbolic, or parabolic?
    $\begingroup$ @VivekanandMohapatra actually, the solutions to simple elliptical PDEs around a small pertubation tend to come out as “blobs”, ellipse-ish, to parabolic PDEs they disperse ever slower like the arms of a parabola, and for hyperbolic they wander off asymptotically straight towards infinity like a hyperbola
  • If we know a system of PDEs is hyperbolic or elliptic or parabolic . . .
    First, I argue that words like elliptic, parabolic, and hyperbolic are used in common discourse by analysts to describe equations or phenomena via implicit analogy, and that analogy is how we think about PDE most of the time The truth is that we do not understand PDE very well
  • Connection between hyperbola and hyperbolic functions
    The hyperbolic angle is not included between any two lines $$ \theta_h= A a^2 = \frac12\; \log (\tan(π 4+θ_e)):$$ This area relation is found by direct integration It is difficult for me to justify full cross-validity without going into definitions of lengths and hence the dependent hyperbolic angles in any one model of the hyperbolic
  • Hyperbolic curve and hyperbola? - Mathematics Stack Exchange
    Now, why hyperbolic surfaces are called hyperbolic is a separate question One reason maybe is because of the hyperboloid model of the hyperbolic plane However, it appears that the terminology hyperbolic plane was first introduced by Felix Klein in 1871, before the hyperboloid model was known
  • What are the interesting applications of hyperbolic geometry?
    the hyperbolic plane In particular, the hyperbolic plane is the universal cover of every Riemann surface of genus two or higher This fact is centrally important all over mathematics This is why you have to learn about hyperbolic geometry to study modular forms in number theory, for instance
  • How to determine where a non-linear PDE is elliptic, hyperbolic, or . . .
    I'm trying to understand the classification of PDEs into the categories elliptic, hyperbolic, and parabolic Frustratingly, most of the discussions I've found are "definition by examples '' I think I more or less understand this classification in the case of quasi-linear second-order PDE, which is what's described on Wikipedia
  • How do you explain what a hyperbolic PDE is. . . ?
    This is in stark contrast to the parabolic PDE, where immediately the whole system noticed a difference Thus, hyperbolic systems exhibit finite speed of propagation (of information) In contrast, for the parabolic heat equation, this speed was infinite!





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