Displaying similar documents to “Dirac's Principle of Mathematical Beauty, Mathematics of Harmony and 'Golden' Scientific Revolution”

Leonardo Fibonacci and Abbaco Culture. A Proposal to Invert the Roles

Jens Høyrup (2005)

Revue d'histoire des mathématiques

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Since long it has been regarded as an obvious fact in need of no argument that the mathematics of the Italian abbacus school was taken over from Leonardo Fibonacci’s . What does look like an argument is that an abbacus book from the outgoing 13th century (apparently the earliest extant specimen) claims to be made “according to the opinion” of Fibonacci. Close analysis of the text reveals, however, that everything basic is independent of Fibonacci, while the indubitable borrowings from...

Preface

J. Berstel, T. Harju, J. Karhumäki (2008)

RAIRO - Theoretical Informatics and Applications

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An inequality for Fibonacci numbers

Horst Alzer, Florian Luca (2022)

Mathematica Bohemica

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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.

Determinants and inverses of circulant matrices with complex Fibonacci numbers

Ercan Altınışık, N. Feyza Yalçın, Şerife Büyükköse (2015)

Special Matrices

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Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.

The Geometric and Dynamic Essence of Phyllotaxis

P. Atela (2011)

Mathematical Modelling of Natural Phenomena

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We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.

On generalized bihyperbolic Mersenne numbers

Dorota Bród, Anetta Szynal-Liana (2024)

Mathematica Bohemica

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In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.

Gelin-Cesáro identities for Fibonacci and Lucas quaternions

Ahmet Daşdemir (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.

On useful schema in survival analysis after heart attack

Czesław Stępniak (2014)

Discussiones Mathematicae Probability and Statistics

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Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers