Similar Ruled Surfaces with Variable Transformations in the Euclidean 3-space

TL;DR

This paper introduces the concept of similar ruled surfaces in Euclidean 3-space, analyzing their properties and establishing conditions under which developable ruled surfaces are similar based on their striction curves.

Contribution

The study defines similar ruled surfaces and proves that developable ruled surfaces are similar if their striction curves are similar with variable transformation.

Findings

Developable ruled surfaces form a family of similar ruled surfaces under specific conditions.

Striction curves of similar ruled surfaces are related by variable transformation.

Properties of similar ruled surfaces are characterized in Euclidean 3-space.

Abstract

In this study, we define a family of ruled surfaces in the Euclidean 3-space E^3 and called similar ruled surfaces. We obtain some properties of these special surfaces and we show that developable ruled surfaces form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curves with variable transformation.