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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AIMS Press
2024-10-01
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| 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. |
| format | Article |
| id | doaj-art-9efdecc16d844dbaaf93a190599776f3 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| 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 |