Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
Author index
To appear
Other MSP journals
The geometry of some Fibonacci identities in the Hosoya triangle

Rigoberto Flórez, Robinson A. Higuita and Antara Mukherjee

Vol. 16 (2023), No. 2, 183–200

The Hosoya triangle is a triangular array where every entry is a product of two Fibonacci numbers. We use the geometry of this triangle to find new identities related to Fibonacci numbers. We give geometric interpretation for some well-known identities of Fibonacci numbers. For instance, the Cassini identity and the Catalan identity. We also extend some identities that hold in the Pascal triangle to the Hosoya triangle. For example, the hockey stick extends from binomials to products of Fibonacci numbers and the rhombus property extends a binomial identity from the Pascal triangle to an identity of products of Fibonacci numbers in the Hosoya triangle.

Fibonacci numbers, Hosoya triangle, rectangle property, zigzag property, braid property, hockey stick property, Cassini identity, Catalan identity
Mathematical Subject Classification 2010
Primary: 11B39
Secondary: 11B83
Received: 20 January 2018
Revised: 4 May 2022
Accepted: 7 June 2022
Published: 26 May 2023

Communicated by Kenneth S. Berenhaut
Rigoberto Flórez
Department of Mathematical Sciences
The Citadel
Charleston, SC
United States
Robinson A. Higuita
Instituto de Matemáticas
Universidad de Antioquia
Antara Mukherjee
Department of Mathematical Sciences
The Citadel
Charleston, SC
United States