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Mathematical phyllotaxis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical phyllotaxisby Jonathan Swinton.
Author:	Swinton, Jonathan.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xiv, 169 p. :ill. (chiefly col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	PhyllotaxisMathematical models.
Online resource:	https://doi.org/10.1007/978-3-031-94013-2
ISBN:	9783031940132$q(electronic bk.)

Mathematical phyllotaxis
Swinton, Jonathan.

Mathematical phyllotaxis[electronic resource] /by Jonathan Swinton. - Cham :Springer Nature Switzerland :2025. - xiv, 169 p. :ill. (chiefly col.), digital ;24 cm. - Surveys and tutorials in the applied mathematical sciences,v. 172199-4773 ;. - Surveys and tutorials in the applied mathematical sciences ;v.7..

Motivation and outline -- Fibonacci numbers, the golden ratio, and co-prime integers -- Co-primality, continued fractions, and Möbius maps -- The geometry of cylindrical lattices -- Classifying cylindrical lattices -- Transformed Lattices -- Developmental biology of the plant -- Statisical phyllotaxis -- Placement models -- Stacked-disk models -- Some future directions.

For centuries, scientists and mathematicians have sought to explain why Fibonacci numbers appear in plant spirals. In recent decades, a modern consensus framework has emerged, offering a compelling mathematical and biological model that goes beyond Fibonacci structure to explain a variety of plant forms. This book provides a rigorous yet accessible introduction to that framework, spanning the mathematics of the Euclidean algorithm, bifurcation theory, and modern molecular biology. Delving into the mechanics of how plants determine organ placement, the book introduces key mathematical tools to classify and analyze these patterns. It examines classic and contemporary models, from Hofmeister's hypothesis to transporter protein-based auxin mechanisms, evaluating their current effectiveness in explaining the evolution and development of plant design. Written for mathematicians, biologists, and interdisciplinary researchers, Mathematics of Phyllotaxis equips readers with the knowledge to critique and contribute to this evolving field. Whether you're a student, a researcher, or simply fascinated by nature's mathematical beauty, this gorgeously illustrated book offers fresh insights into one of biology's most intriguing mysteries.

ISBN: 9783031940132$q(electronic bk.)

Standard No.: 10.1007/978-3-031-94013-2doiSubjects--Topical Terms:

1005062
Phyllotaxis
--Mathematical models.

LC Class. No.: QK649

Dewey Class. No.: 581.48

Mathematical phyllotaxis
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505 0 $a Motivation and outline -- Fibonacci numbers, the golden ratio, and co-prime integers -- Co-primality, continued fractions, and Möbius maps -- The geometry of cylindrical lattices -- Classifying cylindrical lattices -- Transformed Lattices -- Developmental biology of the plant -- Statisical phyllotaxis -- Placement models -- Stacked-disk models -- Some future directions.
520 $a For centuries, scientists and mathematicians have sought to explain why Fibonacci numbers appear in plant spirals. In recent decades, a modern consensus framework has emerged, offering a compelling mathematical and biological model that goes beyond Fibonacci structure to explain a variety of plant forms. This book provides a rigorous yet accessible introduction to that framework, spanning the mathematics of the Euclidean algorithm, bifurcation theory, and modern molecular biology. Delving into the mechanics of how plants determine organ placement, the book introduces key mathematical tools to classify and analyze these patterns. It examines classic and contemporary models, from Hofmeister's hypothesis to transporter protein-based auxin mechanisms, evaluating their current effectiveness in explaining the evolution and development of plant design. Written for mathematicians, biologists, and interdisciplinary researchers, Mathematics of Phyllotaxis equips readers with the knowledge to critique and contribute to this evolving field. Whether you're a student, a researcher, or simply fascinated by nature's mathematical beauty, this gorgeously illustrated book offers fresh insights into one of biology's most intriguing mysteries.
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