Euler's Identity

How to combine 5 important math constants to a short formula

Max Muster1, Lisa Master2

1Hochschule Gartenstadt
2Universität Übersee
May 2021
Keywords: 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 eix=cosx+isinxe^{ix}=\cos x + i\sin x for any real number xx, we get to Euler's identity with the special case of x=πx = \pi

eiπ+1=0.e^{i\pi}+1=0\,.(1)

The arithmetic operations addition, multiplication and exponentiation combine the fundamental constants

3. Conclusion

It has been shown, how Euler's identity makes a valid formula from five mathematical constants.

References

[1] Euler's identity