Iterative Designs with Similar Triangles

TL;DR

This paper explores how iterative geometric constructions using similar triangles can generate intricate designs, illustrating key mathematical concepts and offering tools for educational exploration.

Contribution

It introduces a simple iterative technique based on similar triangles to create complex geometric designs and educational activities.

Findings

Generated diverse geometric patterns through iteration.

Demonstrated educational value of iterative triangle constructions.

Suggested extensions for further exploration and student projects.

Abstract

One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and introduce important mathematical concepts. We give examples using one of the most common of geometrical constructions, namely, the similar triangle. In the final section, we suggest other possibilities that could be used for guided exploration or for student projects.