Hybrid Number Triplets and a New Polar Representation of Hybrid Numbers

---

Koçay B., TUNCER O. O., GÖK İ., YAYLI Y.

Proceedings of the National Academy of Sciences India Section A - Physical Sciences, cilt.95, sa.3, ss.337-347, 2025 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 95 Sayı: 3
• Basım Tarihi: 2025
• Doi Numarası: 10.1007/s40010-025-00934-x
• Dergi Adı: Proceedings of the National Academy of Sciences India Section A - Physical Sciences
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
• Sayfa Sayıları: ss.337-347
• Anahtar Kelimeler: Complex numbers, Dual numbers, Hybrid numbers, Hyperbolic numbers, Polar form
• Ankara Üniversitesi Adresli: Evet

Özet

Hybrid numbers are defined as a non-commutative number system generalizing the complex, dual, and hyperbolic numbers with the relation. This paper aims to provide new polar representations for hybrid numbers. To achieve this we first introduce truncated hybrid numbers (or hybrid number triplets) obtained by truncating a vector component of a hybrid number. Therefore there are three types of truncated hybrid numbers. Then, we determine the conditions for the multiplication of two truncated hybrid numbers to be closed and commutative. Finally, we use what we call h-truncated hybrid numbers to provide a new polar representation for hybrid numbers. Many numerical examples are provided to support the theory of this paper.