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单词 Euler identity
释义

Euler identity

中文百科

欧拉恒等式 Euler's identity

（重定向自Euler identity）
Fórmula de Euler para un ángulo general.
The exponential function ez can be defined as the limit of (1 + z/N)N, as N approaches infinity, and thus eiπ is the limit of (1 +iπ/N)N. In this animation N takes various increasing values from 1 to 100. The computation of (1 + iπ/N)N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 +iπ/N)N. It can be seen that as N gets larger (1 +iπ/N)N approaches a limit of −1.

欧拉恒等式是指下列的关系式：

e^{i \pi}+1=0\,

其中e\,是自然指数的底，i \,是虚数单位，\pi \,是圆周率。

这条恒等式第一次出现于1748年莱昂哈德·欧拉在洛桑出版的书Introductio \,。这是复分析的欧拉公式的特殊情况。

理乍得·费曼称这恒等式为「数学最奇妙的公式」，因为它把5个最基本的数学常数简洁地连系起来。

英语百科

Euler's identity 欧拉恒等式

（重定向自Euler identity）
The exponential function ez can be defined as the limit of (1 + z/N)N, as N approaches infinity, and thus eiπ is the limit of (1 +iπ/N)N. In this animation N takes various increasing values from 1 to 100. The computation of (1 + iπ/N)N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 +iπ/N)N. It can be seen that as N gets larger (1 +iπ/N)N approaches a limit of −1.
Fórmula de Euler para un ángulo general.

In mathematics, Euler's identity (also known as Euler's equation) is the equality

where

Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered an example of mathematical beauty.
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更新时间：2025/6/17 9:18:29