Hyperbolic Flowers

Abstract

Crochet models of a hyperbolic plane is a popular educational tool as they help to visualize complicated objets in hyperbolic geometry. We present another way how to make crochet models when we view them as a part of a triangulated hyperbolic plane. We also provide a model of a cylinder in a hyperbolic space. This approach helps to understand various properties of hyperbolic geometry that are demonstrated in the paper: a sum of angles and a relation between edges and angles in a hyperbolic triangle, tiling of a hyperbolic plane, ratio of the circumference to the radius of a hyperbolic disc and even Nash-Kuiper embedding theorem. Oriented on students learning basics of Riemannian geometry.