Babadag, FaikAtasoy, Ali2025-01-212025-01-2120242473-6988https://doi.org/10.3934/math.20241480https://hdl.handle.net/20.500.12587/25200In 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.eninfo:eu-repo/semantics/openAccesshyper-dual Pell number; hyper-dual Pell-Lucas number; hyper-dual Pell vector; hyper-dual angleArticle911306553066610.3934/math.202414802-s2.0-85208650479Q1WOS:001346103400001N/A