On Generalized Euler Spirals in E^3

TL;DR

This paper introduces generalized Euler spirals in three-dimensional space, defining them as ratios of rational linear functions and exploring their properties to enhance understanding of their role in differential geometry.

Contribution

It extends the concept of Euler spirals to three dimensions and characterizes these curves using ratios of rational linear functions.

Findings

Defined generalized Euler spirals in E^3.

Provided characterizations of these spirals.

Enhanced understanding of their geometric properties.

Abstract

The Cornu spirals on plane are the curves whose curvatures are linear. Generalized planar cornu spirals and Euler spirals in E^3, the curves whose curvatures are linear are defined in [1,5]. In this study, these curves are presented as the ratio of two rational linear functions. Also here, generalized Euler spirals in E^3 has been defined and given their some various characterizations. The approach I used in this paper is useful in understanding the role of Euler spirals in E^3 in differential geometry.