---
date: '2024-11-05'
description: probably the most beautiful equation in all mathematics
id: Euler's identity
modified: 2026-06-05 15:08:29 GMT-04:00
tags:
  - math
title: Euler's identity
created: '2024-11-05'
published: '2024-11-05'
pageLayout: default
slug: thoughts/Euler's-identity
permalink: https://aarnphm.xyz/thoughts/Euler's-identity.md
generator:
  quartz: v4.6.0
  hostedProvider: Cloudflare
  baseUrl: aarnphm.xyz
full: https://aarnphm.xyz/llms-full.txt
---
$$
\begin{aligned}
e^{i \pi} &+ 1 = 0 \\
\\
\because e &: \text{Euler\unicode{x2019}s number} \\
i &: \text{imaginary unit satisfies } i^{2} = -1 \\
\pi &: \text{pi}
\end{aligned}
$$

Special case of Euler’s formula:

$$
e^{i \theta} = \cos(\theta) + i \sin(\theta)
$$