Geometric proofs and algebraic functions

TL;DR

This paper introduces a hybrid approach combining synthetic and analytic geometry, using polynomial algebra and calculus to simplify proofs of classical Euclidean geometric problems by reducing them to finite cases.

Contribution

It presents a novel method that integrates algebraic and geometric techniques to streamline proofs of Euclidean theorems.

Findings

Reduction of geometric proofs to finite cases

Application of polynomial algebra and calculus in geometry

Simplification of classical Euclidean problem proofs

Abstract

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the proof of some general theorems to a finite number of particular cases.