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Dergiler / Proceedings of International Mathematical Sciences / 2026 / Volume: 7 Issue: 1

On Stakhov Functions and New Hyperboloid Surfaces

Ahmet Daşdemir(kastamonu üniversitesi)0000-0001-8352-2020
Sayfa
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Yayın Tarihi
2025-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Notably, we demonstrate that these surfaces are geodesic.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper presents an investigation into the generalization of hyperbolic Fibonacci sine and cosine functions, as well as Fibonacci spirals.
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Temel Bulgular & Veri:Initially, we establish the main definitions and theoretically model them, listing several special cases.
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Sonuç & Katkı:Notably, we demonstrate that these surfaces are geodesic.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hyperbolic Fibonacci function · Hyperbolic Stakhov function · Stakhov hyperboloid

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.

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Bu Makaleye Atıf Yap

Daşdemir, A. (2025). On Stakhov Functions and New Hyperboloid Surfaces. Proceedings of International Mathematical Sciences, Volume: 7 Issue: 1. https://doi.org/10.47086/pims.1653932

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Kaynakça (11)

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  11. A. F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke. Math. J. 32(3) (1965) 437–446.