V2EX hyperboloid

Hyperboloid

Definition / 释义

hyperboloid(双曲面):一种二次曲面(由二次方程描述的三维曲面),形状常见为“沙漏/冷却塔”样或“两片分离的碗状”。在数学中通常分为单叶双曲面(one-sheet hyperboloid)和双叶双曲面(two-sheet hyperboloid)。

Pronunciation (IPA) / 发音

/haprbld/(美式常见)
/hapbld/(英式常见)

Examples / 例句

A hyperboloid can look like a cooling tower.
双曲面看起来可能像冷却塔。

In analytic geometry, a hyperboloid is defined by a second-degree equation in three variables.
在解析几何中,双曲面由三个变量的二次方程来定义。

Etymology / 词源

hyperboloid 来自 hyperbola(双曲线) + -oid(……状的)。其中 hyperbola 源于希腊语 hyperbolē(“抛掷超过、夸张/超越”之意),**-oid** 表示“形状类似”。整体字面可理解为“类似双曲线(生成的)形状”,对应其与双曲线密切相关的几何性质。

Related Words / 相关词

Literary Works / 文学与著作例证

  • Hilbert & Cohn-Vossen《Geometry and the Imagination》:讨论二次曲面时常涉及双曲面等典型曲面。
  • H. S. M. Coxeter《Introduction to Geometry》:在解析与射影几何相关章节中会出现双曲面等曲面术语。
  • Misner, Thorne & Wheeler《Gravitation》:在相对论与几何模型相关内容中会用到双曲面/双曲几何的表述与模型。
  • 相关双曲几何教材(如以“hyperboloid model/双曲面模型”为主题的章节):常用“hyperboloid”来指代双曲空间的一种经典模型。
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