Differential geometry of space curves: Forgotten chapters

TL;DR

This paper provides a modern, unified treatment of evolutes and involutes of space curves, incorporating new observations and visual illustrations to enhance understanding of classical differential geometry concepts.

Contribution

It offers a contemporary, cohesive perspective on space curve evolutes and involutes, including novel insights and computer graphics visualizations.

Findings

Enhanced understanding of evolutes and involutes

Introduction of novel geometric observations

Visual illustrations using computer graphics

Abstract

We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be useful. The results are illustrated with the help of computer graphics, a tool that was not not available to the classical geometers.