Pi (π) In Nature, Art, and Culture

Geometry as a Hermeneutic Science
Erscheinungsjahr 2020
ISBN: 978-90-04-43337-3
Verlag: Brill

Buch, Englisch, Band 1, 134 Seiten, Format (B × H): 160 mm x 236 mm, Gewicht: 340 g

Reihe: Studies in Mathematics in the Arts and Humanities

In Pi (p) in Nature, Art, and Culture Marcel Danesi revisits the importance of p 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 p, 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.

Autoren/Hrsg.

Danesi, Marcel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

Preface

1. Discovery of p 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

Über Autor(innen)

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.