A Novel Proof of Euler's Formula

This research presents a unique derivation of Euler's formula, \(e^{i\theta} = \cos\theta + i\sin\theta\), discovered through integral manipulation. Explore two versions of the discussion, each offering a different perspective on the proof's profound implications.

Version 1: Concise Derivation

A direct and focused presentation of the proof. This version is ideal for quickly understanding the core mathematical steps and the primary result.

Read Concise Version

Version 2: Expanded Geometric Interpretation

An in-depth exploration that includes the full derivation, extensive geometric discussion, background on complex numbers, and visual aids to build intuition.

Read Expanded Version