Comments on: Intuitive Understanding Of Euler's Formula

By: Federico Ferreres

Federico Ferreres — Sun, 03 Jul 2022 05:27:47 +0000

I come back from time to time to this article like a person that likes a story so much but that's far away from one's daily duties, that takes joy in having forget as many details as possible, just to rediscover them again. The fact this contains 1, e, pi, i and -1, 2 (what's the outcome of growing 1 a 100%?), relates so many key aspects, is just wonderful. Even simple things like the = sign being overloaded was a fantastic bonus, it's so simple that's almost never noted anywhere and it can be confusing/ambiguous anytime one encounters any formula one is unfamiliar with. This is why I enjoy programming so much, but have always felt angst against how math is noted.

By: 傅里叶变换和正弦函数和欧拉公式 - 算法网

傅里叶变换和正弦函数和欧拉公式 - 算法网 — Sun, 05 Sep 2021 19:41:54 +0000

[…] ex=1+x1!+x22!+x33!+⋯cos(x)=1−x22!+x44!−x66!+⋯sin(x)=x−x33!+x55!−x77!+⋯ 将 ex 中的 x 换成 ±ix ，因为 (±i)2=−1,(±i)3=∓i,(±i)4=1,⋯ ，所以 e+xi=1+ix1!−x22!−ix33!+x44!+⋯=(1+x44!−x66!+⋯)+i(x−x33!+x55!−x77!+⋯)=cos(x)+isin(x)e−xi=cos(x)−isin(x) 如果非要理解 e 的 i 次方是什么意思的话，可以参考： https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ […]

By: Mathematics – God’s Second Language – Polymathica

Mathematics – God’s Second Language – Polymathica — Tue, 13 Jul 2021 03:03:57 +0000

[…] https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ […]

By: Yasir

Yasir — Fri, 02 Apr 2021 08:11:19 +0000

Its great intuitive explanation Khalid. One thing missing is why consider i as a separate axis. Secondly I think intuition of Taylor series based proof of identity can also help.

I tried to grasp that intuition in lockdown and put it in form of a video.

https://www.youtube.com/wat...