V2EX conformal mapping

Conformal Mapping

释义 Definition

Conformal mapping保角映射/共形映射。指一种在局部保持角度(更准确地说,保持夹角及其方向)的映射,常见于复分析与几何中;典型例子是复平面上的解析函数(在导数不为零处)所给出的映射。除“保角”外,它一般不保持长度或面积。

发音 Pronunciation (IPA)

/knfrml mp/

例句 Examples

A conformal mapping preserves angles locally.
共形映射在局部保持角度不变。

Using conformal mapping, engineers can transform a complicated boundary into a simpler shape to solve a flow problem.
利用共形映射,工程师可以把复杂边界变换成更简单的形状,从而求解流动问题。

词源 Etymology

conformal 来自拉丁语词根 con-(“共同、一起”)+ form(“形状”),字面含义接近“形状一致/相符合”。在数学语境中,它被专门用来表示“保持角度结构”的性质;mapping 则是“映射、变换”的常用数学术语。合起来即“保持角度结构的映射”。

相关词 Related Words

文献与作品 Literary / Notable Works

  • Complex Analysis(Lars V. Ahlfors)系统讲解共形映射与其在复分析中的核心地位
  • Visual Complex Analysis(Tristan Needham)以几何直观方式介绍共形映射与复变函数
  • Conformal Mapping(Zeev Nehari)以“共形映射”为主题的经典专著
  • Complex Variables and Applications(James Ward Brown & Ruel V. Churchill)包含常见共形映射方法与应用章节
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