The Generalization of Gaussians and Leonardo's Octonions

• Autorzy: Renata Passos Machado Veira , Milena Carolina dos Santos Mangueira , Francisco Régis Vieira Alves , Paula Maria Machado Cruz Catarino
• Języki publikacji: EN

Abstrakty

EN

In order to explore the Leonardo sequence, the process of complexification 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.(original abstract)

Słowa kluczowe

EN

Mathematics; Functional equation

PL

Matematyka; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2023
• Tom: 37 (1)
• Strony: 117--137

Twórcy

autor

Renata Passos Machado Veira

• Federal University of Ceará Fortaleza-CE, Brasil

autor

Milena Carolina dos Santos Mangueira

• Federal University of Ceará, Brasil

autor

Francisco Régis Vieira Alves

• Federal University of Ceará, Brasil

autor

Paula Maria Machado Cruz Catarino

• University of Trás-os-Montes and Alto Douro, Portugal

Bibliografia

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• Vieira R.P.M., Alves F.R.V., and Catarino P.M.M.C., Relações bidimensionais e identidades da sequência de Leonardo, Revista Sergipana de Matemática e Educação Matemática 4 (2019), no. 2, 156-173.
• Vieira R.P.M., Alves F.R.V., and P.M.M.C. Catarino, Uma extensão dos octônios de Padovan para inteiros não positivos, C.Q.D. - Revista Eletrônica Paulista de Matemática 19 (2020), Edição Dezembro, 9-16.
• Vieira R.P.M., Mangueira M.C. dos S., Alves F.R.V., and Catarino P.M.M.C., A forma matricial dos números de Leonardo, Ci. e Nat. 42 (2020), 40 yrs. - Anniv. Ed., Article No. e100, 6 pp.

Identyfikatory

DOI

10.2478/amsil-2023-0004