Geometric 3-space and multiplicative quaternions

Aslan S., Bekar M., Yaylı Y.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.20, no.9, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 9
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219887823501517
  • Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Geometric 3-space, multiplicative quaternions, geometric angle, geometric circle, geometric sphere, geometric rotation
  • Ankara University Affiliated: Yes

Abstract

In this paper, we introduce a new vector space, the three-dimensional geometric real vector space Double-struck capital R-3(G), and a new number system, multiplicative quaternions H(G). We give some basic algebraic properties of these concepts. We define spatial rotation in Double-struck capital R(3()G) by using multiplicative quaternions. Finally, we give an example to illustrate our results.