V2EX real axis

Real axis

Definition / 定义

“实轴”:在复平面(complex plane)中表示实数的那条水平坐标轴。复数 \(a+bi\) 的实部 \(a\) 落在实轴上;与之垂直的是虚轴(imaginary axis)。在很多图像与积分路径中,实轴也常指“沿 \(y=0\) 的那条线”。

Pronunciation / 发音

/ril kss/

Examples / 例句

Plot the point on the real axis.
把这个点画在实轴上。

In the complex plane, numbers with zero imaginary part lie on the real axis, while a small imaginary component moves them off it.
在复平面中,虚部为零的数都落在实轴上;只要加入很小的虚部,就会使它们偏离实轴。

Etymology / 词源

real 来自拉丁语 realis(“真实的、实在的”),与 res(“事物”)相关;axis 来自拉丁语 axis(“轴、车轴”)。在数学里,“real axis”字面意思就是“表示实数的轴”,用于把“实数方向”与“虚数方向”清晰区分。

Related Words / 相关词

Literary Works / 文学作品

  • Complex Analysis Lars V. Ahlfors(经典复分析教材中频繁使用“real axis”描述复平面与积分路径)
  • Complex Variables and Applications James Ward Brown & Ruel V. Churchill(用“real axis / imaginary axis”讲解复变量函数与映射)
  • Visual Complex Analysis Tristan Needham(通过图像直观解释复平面中的实轴与虚轴)
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