Applications of Equivalent Curves to Ruled Surfaces

Bataray B., Camcı Ç.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.18, no.1, pp.135-142, 2025 (ESCI)

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.36890/iejg.1528951
  • Journal Name: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.135-142
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

In this paper, the characterization of equivalent curves in E^3 is used to define ruled surfaces whose base curves are equivalent curves and to examine the relationships between them. At the same time, an equivalence relation for ruled surfaces is obtained. The equivalence classes resulting from this relation are studied. It is concluded that all ruled surfaces in the equivalence class of a developable surface are developable. Thus, a method is established to obtain an infinite ruled surface from a ruled surface. Finally, a new method is given to obtain a developable surface.