Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces

Barış Ateş

doi:10.33434/cams.1766078

EN

Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces

Abstract

In the present work, the inverse stereographic projection of Fibonacci points onto quadric surfaces of revolution is investigated. The construction of Fibonacci points from Fibonacci numbers, together with the one-to-one and invertible nature of stereographic projection, enables the establishment of new mathematical relations on quadric surfaces.} Cassini and Catalan identities are analyzed and mapped onto quadric surfaces to demonstrate how classical identities transform under this mapping, thereby opening new application areas for Fibonacci numbers on the surface of quadrics. In two dimensional plane, in addition to points, special Fibonacci related grids, circles, and spirals are considered. Their inverse stereographic projections are obtained. It is shown that the surfaces of quadrics can be partitioned into special domains whose boundaries can be fully expressed in terms of Fibonacci related curves. Because quadric surfaces frequently appear in botanical structures, these new relations may provide new insights into the biological applications of Fibonacci numbers in developmental biology.

Keywords

Fibonacci points, Stereographic projection, Quadric surfaces

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

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

Early Pub Date

February 20, 2026

Publication Date

February 20, 2026

Submission Date

August 15, 2025

Acceptance Date

January 27, 2026

Published in Issue

Year 2026 Volume: 9 Number: 1

DOI

https://doi.org/10.33434/cams.1766078

IZ

https://izlik.org/JA98TZ95UG

APA

Ateş, B. (2026). Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces. Communications in Advanced Mathematical Sciences, 9(1), 34-49. https://doi.org/10.33434/cams.1766078

AMA

1.Ateş B. Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces. Communications in Advanced Mathematical Sciences. 2026;9(1):34-49. doi:10.33434/cams.1766078

Chicago

Ateş, Barış. 2026. “Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces”. Communications in Advanced Mathematical Sciences 9 (1): 34-49. https://doi.org/10.33434/cams.1766078.

EndNote

Ateş B (March 1, 2026) Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces. Communications in Advanced Mathematical Sciences 9 1 34–49.

IEEE

[1]B. Ateş, “Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces”, Communications in Advanced Mathematical Sciences, vol. 9, no. 1, pp. 34–49, Mar. 2026, doi: 10.33434/cams.1766078.

ISNAD

Ateş, Barış. “Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces”. Communications in Advanced Mathematical Sciences 9/1 (March 1, 2026): 34-49. https://doi.org/10.33434/cams.1766078.

JAMA

1.Ateş B. Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces. Communications in Advanced Mathematical Sciences. 2026;9:34–49.

MLA

Ateş, Barış. “Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces”. Communications in Advanced Mathematical Sciences, vol. 9, no. 1, Mar. 2026, pp. 34-49, doi:10.33434/cams.1766078.

Vancouver

1.Barış Ateş. Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces. Communications in Advanced Mathematical Sciences. 2026 Mar. 1;9(1):34-49. doi:10.33434/cams.1766078

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Abstract

Inverse Stereographic Projection of Fibonacci Points onto the Quadric Surfaces

Abstract

Keywords

References

Details

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Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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