学习笔记《Euler's formula》

作者: 马文Marvin | 来源:发表于2018-04-04 11:49 被阅读36次

学习笔记《Euler's formula》
克里斯安德森：TED演讲的秘密
日本人的“人生满意度公式”
Lesson8 揭秘TED演讲背后的那些套路 TED’s sec
Turn the car
Chapter 7 -- Performance Analysi
Notion笔记Formula
Go to bed smarter than when you
2017-10-25
Day 1 1-1 Wednesday 2019-01-16

欧拉公式建立了三角函数和复平面指数函数之间的关系，是复变函数的基础

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x

e^ix = cos(x) + i*sin(x)

欧拉恒等式（Euler's Identity）e^iπ + 1 = 0 是 Euler's formula 当 x = π 时候的特殊情况

虽然这个等式被称为欧拉恒等式，但是应该是 Roger Cotes 首先发现的：

It has been claimed that Euler's identity appears in his monumental work of mathematical analysis published in 1748, Introductio in analysin infinitorum. However, it is questionable whether this particular concept can be attributed to Euler himself, as he may never have expressed it. (Moreover, while Euler did write in the Introductio about what we today call Euler's formula, which relates e with cosine and sine terms in the field of complex numbers, the English mathematician Roger Cotes (who died in 1716, when Euler was only 9 years old) also knew of this formula and Euler may have acquired the knowledge through his Swiss compatriot Johann Bernoulli.)