A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION

Barış Ateş; Selcan Ateş; Alp Kuştepeli

A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION

Abstract

In this study, a new geometric framework for Fibonacci numbers is introduced through the definition of Fibonacci points, whose components are Fibonacci numbers. These points are then mapped onto the sphere by means of inverse stereographic projection (ISP), providing novel recurrence relations and algebraic structures analogous to those in classical ones. The transformation of Fibonacci-related geometrical entities such as lines and circles is investigated, leading to the definition of new spherical regions associated with Fibonacci parallels and meridians. Furthermore, a deformed version of the Binet–Fibonacci spiral passing through the Fibonacci points is constructed, which may offer applications in modeling biological spiral deviations caused by environmental effects. Classical Fibonacci identities, such as Cassini identities, are revisited in this spherical setting, and their transformations are established. Finally, possible generalizations of these results to higher-dimensional spaces are discussed.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory, Real and Complex Functions (Incl. Several Variables)

Journal Section

Research Article

Authors

Barış Ateş ^*
0000-0002-8138-7360
Türkiye

Selcan Ateş
0000-0002-0078-0647
Türkiye

Alp Kuştepeli
0000-0002-8995-6628
Türkiye

Publication Date

August 7, 2026

Submission Date

May 17, 2025

Acceptance Date

November 3, 2025

Published in Issue

Year 2026 Volume: 16 Number: 8

IZ

https://izlik.org/JA25SF75CB

Cite

RIS / Bibtex

APA

Ateş, B., Ateş, S., & Kuştepeli, A. (2026). A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION. TWMS Journal of Applied and Engineering Mathematics, 16(8), 938-952. https://izlik.org/JA25SF75CB

AMA

1.Ateş B, Ateş S, Kuştepeli A. A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION. JAEM. 2026;16(8):938-952. https://izlik.org/JA25SF75CB

Chicago

Ateş, Barış, Selcan Ateş, and Alp Kuştepeli. 2026. “A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION”. TWMS Journal of Applied and Engineering Mathematics 16 (8): 938-52. https://izlik.org/JA25SF75CB.

EndNote

Ateş B, Ateş S, Kuştepeli A (August 1, 2026) A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION. TWMS Journal of Applied and Engineering Mathematics 16 8 938–952.

IEEE

[1]B. Ateş, S. Ateş, and A. Kuştepeli, “A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION”, JAEM, vol. 16, no. 8, pp. 938–952, Aug. 2026, [Online]. Available: https://izlik.org/JA25SF75CB

ISNAD

Ateş, Barış - Ateş, Selcan - Kuştepeli, Alp. “A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION”. TWMS Journal of Applied and Engineering Mathematics 16/8 (August 1, 2026): 938-952. https://izlik.org/JA25SF75CB.

JAMA

1.Ateş B, Ateş S, Kuştepeli A. A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION. JAEM. 2026;16:938–952.

MLA

Ateş, Barış, et al. “A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 8, Aug. 2026, pp. 938-52, https://izlik.org/JA25SF75CB.

Vancouver

1.Barış Ateş, Selcan Ateş, Alp Kuştepeli. A NOVEL APPROACH TO THE FIBONACCI NUMBERS BY INVERSE STEREOGRAPHIC PROJECTION. JAEM [Internet]. 2026 Aug. 1;16(8):938-52. Available from: https://izlik.org/JA25SF75CB