Exploring Mathematics with Curvagon Tiles

TL;DR

Curvagons are flexible polygon tiles that enable the construction of complex geometric shapes like hyperbolic surfaces and tori, enhancing hands-on learning of advanced mathematical concepts.

Contribution

Introduction of flexible Curvagon tiles that expand the possibilities of physical geometric modeling beyond rigid plastic tiles.

Findings

Allow construction of hyperbolic surfaces and tori

Facilitate teaching of advanced geometry concepts

Enable creative exploration of mathematical shapes

Abstract

Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like volume, tessellations, and Platonic solids. However, since these tiles are made of hard plastic, they are not very suitable for creating hyperbolic surfaces or shapes where the tiles need to bend. Curvagons are flexible regular polygon building blocks that allow you to quickly build anything from hyperbolic surfaces and tori to dinosaurs and shoes. They can be used to introduce mathematical concepts from Archimedean solids to Gauss-Bonnet theorem. You can also let your imagination run free and build whatever comes to mind.