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.
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.
Jonathan Swinton has worked for thirty years as a mathematical biologist in university plant science and zoology departments and in the pharmaceutical industry. He is a long erstwhile Fellow of Kings College Cambridge and nearly as erstwhile Visiting Professor in Systems Biology in the University of Oxford. Mathematical Phyllotaxis is based on invited graduate lectures that Jonathan gave in the University of Cambridge from 2019 onwards. His social and intellectual group biography Alan Turings Manchester was published in 2018. Shining Molly, his new biography of the psychologist Molly Harrower, has been accepted for publication by the University of Akron Press in 2025.
