---
"lang": "en",
"title": "Euler's Identity",
"subtitle": "How to combine 5 important math constants to a short formula",
"authors": ["Max Muster^{1}", "Lisa Master^{2}"],
"adresses": ["^{1}Hochschule Gartenstadt","^{2}Universität 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](#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
[1] [Euler's identity](https://en.wikipedia.org/wiki/Euler%27s_identity)