V2EX hypersphere

Hypersphere

Definition / 定义

超球(面):在更高维空间中的“球”。通常指 n 维球面(n-sphere),即到某个中心点距离固定的所有点组成的集合;也常用于指其内部对应的“超球体”。(在不同学科/语境中,可能更偏指“超球面”或“超球体”。)

Pronunciation / 发音

/haprsfr/

Examples / 例句

A hypersphere is a sphere in four or more dimensions.
超球是存在于四维或更高维度中的“球”。

In high-dimensional data analysis, points can concentrate near the surface of a hypersphere, which affects how distance-based methods behave.
在高维数据分析中,点可能会“集中”在超球表面附近,从而影响基于距离的方法的表现。

Etymology / 词源

由前缀 **hyper-**(意为“超、超过;更高层次”,源自希腊语 hyper)+ sphere(“球体/球面”,源自希腊语 sphaira,意为“球”)构成,字面意思就是“更高维度的球”。

Related Words / 相关词

Literary Works / 文学作品

  • The Fourth Dimension: Toward a Geometry of Higher Reality Rudy Rucker
  • Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension Michio Kaku
  • The Shape of Space Jeffrey R. Weeks
  • Gdel, Escher, Bach: An Eternal Golden Braid Douglas R. Hofstadter
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