An App for the Discovery of Properties of Poncelet Triangles

TL;DR

This paper introduces a free, browser-based interactive app for exploring Poncelet triangles, allowing users to visualize loci, identify conics, and test metric invariants through numerous customizable experiments.

Contribution

It presents a novel, accessible tool for dynamic geometry exploration of Poncelet triangles with extensive pre-made experiments and sharing capabilities.

Findings

Responsive visualization of Poncelet loci

Identification of conic curves in the geometry

Conservation of metric quantities in experiments

Abstract

We describe a newly-developed, free, browser-based application, for the interactive exploration of the dynamic geometry of Poncelet families of triangles. The main focus is on responsive display of the beauteous loci of centers of such families, refreshing them smoothly upon any changes in simulation parameters. The app informs the user when curves swept are conics and reports if certain metric quantities are conserved. Live simulations can be easily shared via a URL. A list of more than 400 pre-made experiments is included which can be regarded as conjectures and/or exercises. Millions of experiment combinations are possible.