TY  - JOUR
T1  - On Stakhov Functions and New Hyperboloid Surfaces
AU  - Daşdemir, Ahmet
PY  - 2025
DA  - June
Y2  - 2025
DO  - 10.47086/pims.1653932
JF  - Proceedings of International Mathematical Sciences
JO  - PIMS
PB  - İbrahim ÇANAK
WT  - DergiPark
SN  - 2717-6355
SP  - 16
EP  - 27
VL  - 7
IS  - 1
LA  - en
AB  - 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.
KW  - Hyperbolic Fibonacci function
KW  - Hyperbolic Stakhov function
KW  - Stakhov hyperboloid
KW  - Gauss curvature
KW  - Fibonacci hyperboloid
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UR  - https://doi.org/10.47086/pims.1653932
L1  - https://dergipark.org.tr/en/download/article-file/4673147
ER  -