# Construction of curve pairs and their applications

## TL;DR

This paper presents a novel approach to constructing and analyzing curve pairs using integral curves, offering new methods for generating partner curves and exploring their applications in various geometric contexts.

## Contribution

It introduces new techniques for constructing partner curves of a unit speed curve and explores their applications to helices, slant helices, and plane curves.

## Key findings

- New methods for constructing involute-evolute, Mannheim, and Bertrand curves
- Applications to helices, slant helices, and plane curves
- Enhanced understanding of curve pair relationships

## Abstract

In this study, we introduce a new approach to curve pairs by using integral curves. We consider the direction curve and donor curve to study curve couples such as involute-evolute curves, Mannheim partner curves and Bertrand partner curves. We obtain new methods to construct partner curves of a unit speed curve and give some applications related to helices, slant helices and plane curves.

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Source: https://tomesphere.com/paper/1701.04812