V2EX quadric

Quadric

释义 Definition

quadric(四次曲面/二次曲面):在数学中,指由二次方程描述的曲线或曲面,常见于解析几何与代数几何中,例如球面、椭球面、抛物面、双曲面等。(在更高维也可指“二次超曲面”。)

发音 Pronunciation

/kwdrk/

例句 Examples

A sphere is a quadric surface.
球面是一种二次曲面。

In analytic geometry, many shapeslike ellipsoids and hyperboloidscan be described as quadrics defined by second-degree equations.
在解析几何中,许多形状(如椭球面和双曲面)都可以看作由二次方程定义的二次曲面。

词源 Etymology

来自拉丁语 quadr-(“四”)相关词根,经过新拉丁语/科学拉丁语的构词传统形成 quadric。在数学语境里,它与“二次(second-degree)”密切相关:所谓 quadric 通常指由二次项构成的方程所定义的几何对象。

相关词 Related Words

文学/著作中的用例 Literary Works

  • George Salmon, A Treatise on the Analytic Geometry of Three Dimensions(经典解析几何教材中系统讨论二次曲面/quadric surfaces)
  • H.S.M. Coxeter, Introduction to Geometry(几何学名著中涉及二次曲线与二次曲面相关内容)
  • Robin Hartshorne, Algebraic Geometry(代数几何经典教材中使用 quadric 指二次超曲面/二次簇)
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