--- "lang": "en", "title": "Euler's Identity", "subtitle": "How to combine 5 important math constants to a short formula", "authors": ["Max Muster1", "Lisa Master2"], "adresses": ["1Hochschule Gartenstadt","2Universität Übersee"], "date": "May 2021", "description": "mdmath LaTeX demo site", "tags": ["markdown+math","VSCode","static page","publication","LaTeX","math"] --- ### Abstract Euler's identity makes a valid formula out of five mathematical constants. ## 1. Introduction Euler's identity is often cited as an example of deep mathematical beauty. Three basic arithmetic operations occur exactly once and combine five fundamental mathematical constants [(#1)]. ## 2. The Identity Starting from Euler's formula $e^{ix}=\cos x + i\sin x$ for any real number $x$, we get to Euler's identity with the special case of $x = \pi$ $$e^{i\pi}+1=0\,.$$ (1) The arithmetic operations *addition*, *multiplication* and *exponentiation* combine the fundamental constants * the additive identity $0$. * the multiplicative identity $1$. * the circle constant $\pi$. * Euler's number $e$. * the imaginary constant $i$. ## 3. Conclusion It has been shown, how Euler's identity makes a valid formula from five mathematical constants. ### References  [Euler's identity](https://en.wikipedia.org/wiki/Euler%27s_identity)