Pythagoras, Binomial, and de Moivre Revisited Through Differential Equations

TL;DR

This paper explores classical mathematical theorems like Pythagoras, binomial, and de Moivre's formula through the lens of differential equations, offering a novel perspective on their derivations.

Contribution

It introduces a differential equations approach to derive fundamental theorems traditionally proved through algebraic methods.

Findings

Unified framework for classical theorems using differential equations

New proofs based on initial value problem uniqueness theorems

Enhanced understanding of the connection between geometry, algebra, and differential equations

Abstract

The classical Pythagoras theorem, binomial theorem, de Moivre's formula, and numerous other deductions are made using the uniqueness theorem for the initial value problems in linear ordinary differential equations.