Crochet representation of the Lobachevskian surface

TL;DR

This paper explores crochet models as tangible representations of Lobachevskian surfaces, aiming to connect physical crochet models with non-Euclidean geometry through parametrization.

Contribution

It introduces a parametrization method linking crochet models to non-Euclidean geometries, advancing understanding of their mathematical properties.

Findings

Parametrization of Lobachevskian surfaces via crochet models

Enhanced understanding of non-Euclidean representations

Potential for educational and visualization tools

Abstract

Beginning the study of non-Euclidean geometries, physical models or representations, such as crochet ones, provide a tangible portrayal of these advanced mathematical concepts. However, their connection to local Euclidean surfaces still needs further investigation. This work aims to explore how the characteristics of crochet models relate to non-Euclidean concepts by providing a parametrization of such surfaces.