Danesi Marcel. Pi (π) in Nature, Art, and Culture. Geometry as a Hermeneutic Science

Leiden: Brill, 2021. — 144 p. — (Studies in Mathematics in the Arts and Humanities 1).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.Discovery of π and Its Manifestations
Prologue
Discovery, Calculation, Proof
Geometric Archetypes
Manifestations of Archetypal Structure
Geometry as a Hermeneutic Science
Epilogue
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
Pi in Art and Architecture
Prologue
Pythagoreanism in Art
The Circle in Art and Symbolism
Pi in Art
Epilogue
Pii in Popular Culture
Prologue
Mathematics in Popular Culture
Pi in Popular Culture
Pi-Mania
Epilogue
Order and Chaos
Prologue
Cohen’s Dilemma
Chaos Theory
Order and Chaos
Epilogue
Final Remarks