Pi (π) in Nature, Art, and Culture

Geometry as a Hermeneutic Science

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Author: Marcel Danesi
In Pi (π) in Nature, Art, and Culture Marcel Danesi revisits the importance of π as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle.

Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.

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Marcel Danesi, Ph.D. (1974), is Professor of Semiotics and Linguistic Anthropology at the University of Toronto. He has published extensively in the field of mathematical cognition and education, and founded a center at the Fields Institute for Research in Mathematical Sciences to study the relation between mathematics, the mind, and culture.
"Het voortreffelijke boek laat alle lezers op fascinerende wijze kennismaken met het wonder van π. Pi, of de verhouding van de omtrek van een cirkel tot de diameter, was een van de eerste irrationele getallen die werden ontdekt." [An exccellent book which introduces the author to the wonders of Pi.]
-- Jan M. Broeders, Optische Fenomenen, newsletter 405, March 2021
Preface

1. Discovery of π and Its Manifestations
Prologue
Discovery, Calculation, Proof
Geometric Archetypes
Manifestations of Archetypal Structure
Geometry as a Hermeneutic Science
Epilogue

2. Pi in Mathematics and the Physical World
Prologue
Pythagoreanism
Uniting Arithmetic and Geometry
The Planetary Orbits
Natural and Physical Phenomena
Topology, Non-Euclidean Geometry, and Fractal Geometry
Epilogue

3. Pi in Art and Architecture
Prologue
Pythagoreanism in Art
The Circle in Art and Symbolism
Pi in Art
Epilogue

4. Pi in Popular Culture
Prologue
Mathematics in Popular Culture
Pi in Popular Culture
Pi-Mania
Epilogue

5. Order and Chaos
Prologue
Cohen’s Dilemma
Chaos Theory
Order and Chaos
Epilogue
Final Remarks

References
Index
All interested in mathematics as a tool for investigating reality, and anyone researching the nature of mathematics as a hermeneutic tool. The book is non-technical so that a general audience may also be interested in its approach to geometry.