On hyper-dual vectors and angles with Pell, Pell-Lucas numbers

In this paper, we introduce two types of hyper-dual numbers with components including Pell and Pell-Lucas numbers. This novel approach facilitates our understanding of hyper-dual numbers and properties of Pell and Pell-Lucas numbers. We also investigate fundamental properties and identities associat...

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Main Authors: Faik Babadağ, Ali Atasoy
Format: Article
Language:English
Published: AIMS Press 2024-10-01
Series:AIMS Mathematics
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Online Access:https://www.aimspress.com/article/doi/10.3934/math.20241480?viewType=HTML
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author Faik Babadağ
Ali Atasoy
author_facet Faik Babadağ
Ali Atasoy
author_sort Faik Babadağ
collection DOAJ
description In this paper, we introduce two types of hyper-dual numbers with components including Pell and Pell-Lucas numbers. This novel approach facilitates our understanding of hyper-dual numbers and properties of Pell and Pell-Lucas numbers. We also investigate fundamental properties and identities associated with Pell and Pell-Lucas numbers, such as the Binet-like formulas, Vajda-like, Catalan-like, Cassini-like, and d'Ocagne-like identities. Furthermore, we also define hyper-dual vectors by using Pell and Pell-Lucas vectors and discuse hyper-dual angles. This extensionis not only dependent on our understanding of dual numbers, it also highlights the interconnectedness between integer sequences and geometric concepts.
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series AIMS Mathematics
spelling doaj-art-9efdecc16d844dbaaf93a190599776f32025-08-20T02:12:38ZengAIMS PressAIMS Mathematics2473-69882024-10-01911306553066610.3934/math.20241480On hyper-dual vectors and angles with Pell, Pell-Lucas numbersFaik Babadağ 0Ali Atasoy 11. Department of Mathematics, Kırıkkale University, 71450, Yahşihan, Kırıkkale, Turkey2. Keskin Vocational School, Kırıkkale University, 71800, Keskin, Kırıkkale, TurkeyIn this paper, we introduce two types of hyper-dual numbers with components including Pell and Pell-Lucas numbers. This novel approach facilitates our understanding of hyper-dual numbers and properties of Pell and Pell-Lucas numbers. We also investigate fundamental properties and identities associated with Pell and Pell-Lucas numbers, such as the Binet-like formulas, Vajda-like, Catalan-like, Cassini-like, and d'Ocagne-like identities. Furthermore, we also define hyper-dual vectors by using Pell and Pell-Lucas vectors and discuse hyper-dual angles. This extensionis not only dependent on our understanding of dual numbers, it also highlights the interconnectedness between integer sequences and geometric concepts.https://www.aimspress.com/article/doi/10.3934/math.20241480?viewType=HTMLhyper-dual pell numberhyper-dual pell-lucas numberhyper-dual pell vectorhyper-dual angle
spellingShingle Faik Babadağ
Ali Atasoy
On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
AIMS Mathematics
hyper-dual pell number
hyper-dual pell-lucas number
hyper-dual pell vector
hyper-dual angle
title On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
title_full On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
title_fullStr On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
title_full_unstemmed On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
title_short On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
title_sort on hyper dual vectors and angles with pell pell lucas numbers
topic hyper-dual pell number
hyper-dual pell-lucas number
hyper-dual pell vector
hyper-dual angle
url https://www.aimspress.com/article/doi/10.3934/math.20241480?viewType=HTML
work_keys_str_mv AT faikbabadag onhyperdualvectorsandangleswithpellpelllucasnumbers
AT aliatasoy onhyperdualvectorsandangleswithpellpelllucasnumbers