歐拉恆等式

e ^ (πi) + 1 = 0

歐拉恆等式是指下列的關係式

开始,以相对速度i,走π长时间,加1,则到达原点

其中自然對數的底虛數單位,圓周率

這條恆等式第一次出現於1748年,瑞士數學、物理學家萊昂哈德·歐拉Leonhard Euler)在洛桑出版的書《无穷小分析引论》(Introductio in analysin infinitorum)。這是複分析歐拉公式之特殊情況。

證明

 歐拉公式
 (代入 
 (因  
 

與歐拉恆等式有關的文學作品

博士熱愛的算式》(博士の愛した数式),小川洋子著,臺灣版本由王蘊潔翻譯,二版,麥田出版社,2008年,ISBN 978-986-173-408-8

参见

參考文獻

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