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单词 asymptote
释义

Definition of asymptote in English:

asymptote

noun ˈasɪm(p)təʊtˈæsəm(p)ˌtoʊt
  • A straight line that continually approaches a given curve but does not meet it at any finite distance.

    渐近线

    Example sentencesExamples
    • It simply means that, like a lot of science, absolute and mechanical objectivity is an asymptote we must always approach without quite reaching.
    • Like the asymptote, you are always approaching your goal, but you never achieve it.
    • These models, which more closely resemble reality, involve one or two curves tending towards asymptotes.
    • She was up in her attic one afternoon, trying to concentrate on where to place her asymptotes on her hyperbola, but her mind traveled elsewhere.
    • In book two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies how to draw tangents to given conics.

Derivatives

  • asymptotic

  • adjective ˌasɪm(p)ˈtɒtɪkˌæsəm(p)ˈtɑdɪk
    • Gromov brought his geometric intuition to group theory and told us to look at the asymptotic properties of the Cayley graph.
      Example sentencesExamples
      • He also worked on asymptotic analysis, fractional integration and singular partial differential equations.
      • He often returned to the topic of his first research paper on the error term in an asymptotic formula discovered by Gauss.
      • He gave a wonderful series of lectures on special functions, asymptotic analysis, and approximation theory.
      • Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure.
      • For these data, the linear and asymptotic curves were nearly indistinguishable.
      • Other topics in the large range of applied mathematics topics which he studied were existence theorems and asymptotic expansions.
  • asymptotically

  • adverbasɪm(p)ˈtɒtɪk(ə)li
    • The statement that this function gets asymptotically closer to the actual number of primes as the numbers get bigger is known as the Prime Number Theorem.
      Example sentencesExamples
      • These models are then compared using likelihood ratio tests, for which the test statistic asymptotically follows a distribution.
      • Many statistical methods produce unbiased or asymptotically unbiased estimates of parameters.
      • The polynomial structures are unable to handle correlation patterns that decrease asymptotically to zero within the range of the data, and the correlation obtained by both models goes negative.
      • There seems to be some kind of law that requires presidential campaigns to become asymptotically more trivial as election day approaches.
      • As resource input rates decreased, this proportion increased asymptotically.

Origin

Mid 17th century: from modern Latin asymptota (linea) '(line) not meeting', from Greek asumptōtos 'not falling together', from a- 'not' + sun 'together' + ptōtos 'apt to fall' (from piptein 'to fall').

Definition of asymptote in US English:

asymptote

nounˈasəm(p)ˌtōtˈæsəm(p)ˌtoʊt
  • A line that continually approaches a given curve but does not meet it at any finite distance.

    渐近线

    Example sentencesExamples
    • In book two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies how to draw tangents to given conics.
    • She was up in her attic one afternoon, trying to concentrate on where to place her asymptotes on her hyperbola, but her mind traveled elsewhere.
    • It simply means that, like a lot of science, absolute and mechanical objectivity is an asymptote we must always approach without quite reaching.
    • These models, which more closely resemble reality, involve one or two curves tending towards asymptotes.
    • Like the asymptote, you are always approaching your goal, but you never achieve it.

Origin

Mid 17th century: from modern Latin asymptota (linea) ‘(line) not meeting’, from Greek asumptōtos ‘not falling together’, from a- ‘not’ + sun ‘together’ + ptōtos ‘apt to fall’ (from piptein ‘to fall’).

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更新时间:2024/12/27 16:57:16