Fibonacci Sequences in the Möbius Gyrovector Space
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.7266Keywords:
Fibonacci sequence, gyrogroup, gyrovector space, Möbius additon, hyperbolic geometryAbstract
Let G be a non-empty set, and let ⋆ be a binary operation on G. In (G, ⋆) with a, b ∈ G, the right-Fibonacci sequence generated by a and b is the sequence F0, F1, . . . , Fn, . . . defined by the recurrence relation F0 = a, F1 = b, and Fn = Fn−2 ⋆ Fn−1 for all integers n ≥ 2. In this article, we focus on right-Fibonacci sequences in the M¨obius gyrovector space (D, ⊕M, ⊗M), with particular attention to the convergence of sequences generated by a and b, where a and b are on the same diameter of the open unit disk D in the complex plane. It turns out that such sequences converge to a/|a|, or b/|b|, or 0, depending on relationships among a, b, and the golden ratio.
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Copyright (c) 2026 Rasimate Maungchang, Tarid Suwansri, Teerapong Suksumran
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