On Euler's inequality and automated reasoning with dynamic geometry

TL;DR

This paper explores a novel approach to investigating Euler's inequality using implicit loci in GeoGebra, combining symbolic, numerical, and GPU-accelerated methods to enhance understanding of geometric properties.

Contribution

It introduces a new method integrating symbolic and numerical techniques with GPU acceleration for analyzing geometric inequalities in dynamic geometry environments.

Findings

Implicit locus computation reveals unexpected algebraic curves.

GPU-accelerated web application improves understanding of geometric inequalities.

A combined symbolic and numerical approach offers new insights into Euler's inequality.

Abstract

Euler's inequality $R\geq 2r$ can be investigated in a novel way by using implicit loci in GeoGebra. Some unavoidable side effects of the implicit locus computation introduce unexpected algebraic curves. By using a mixture of symbolic and numerical methods a possible approach is sketched up to investigate the situation. By exploiting fast GPU computations, a web application written in CindyJS helps in understanding the situation even better.