The Generalization of Gaussians and Leonardo’s Octonions

Annales Mathematicae Silesianae

article

Renata Passos Machado Vieira¹  Milena Carolina dos Santos Mangueira²  Francisco Régis Vieira Alves²  Paula Maria Machado Cruz Catarino³ 

[1] Federal University of Ceará Fortaleza-CE Brasil;Federal Institute of Ceará Fortaleza-CE Brasil;University of Trás-os-Montes and Alto Douro Vila Real Portugal

关键词: matrix form;    Binet’s formula;    Gaussian;    octonions;    Leonardo sequence;   

DOI  :  10.2478/amsil-2023-0004

学科分类：内科医学

来源: Walter de Gruyter GmbH

【 摘 要 】

In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented. Also, the recurrence, generating function, Binet’s formula, and matrix form of Leonardo’s Gaussian and octonion numbers are defined. The development of the Gaussian numbers is performed from the insertion of the imaginary component i in the one-dimensional recurrence of the sequence. Regarding the octonions, the terms of the Leonardo sequence are presented in eight dimensions. Furthermore, the generalizations and inherent properties of Leonardo’s Gaussians and octonions are presented.

【 授权许可】

CC BY