On Stakhov Functions and New Hyperboloid Surfaces

Year 2025, Volume: 7 Issue: 1, 16 - 27, 30.06.2025

Ahmet Daşdemir

https://doi.org/10.47086/pims.1653932

Abstract

This paper presents an investigation into the generalization of hyperbolic Fibonacci sine and cosine functions, as well as Fibonacci spirals. Initially, we establish the main definitions and theoretically model them, listing several special cases. We then uncover fundamental results, including the De Moivre and Pythagorean formulas. Based on these new definitions, we introduce new classes of three-dimensional hyperboloid surfaces and compute their Gauss and mean curvatures. Notably, we demonstrate that these surfaces are geodesic.

Keywords

Hyperbolic Fibonacci function , Hyperbolic Stakhov function , Stakhov hyperboloid , Gauss curvature , Fibonacci hyperboloid

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