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Pi () in Nature, Art, and Culture: Geometry as a Hermeneutic Science [Hardback]

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Citas grāmatas par šo tēmu:
In Pi () in Nature, Art, and Culture Marcel Danesi revisits the importance of 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 , 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.

Recenzijas

"Het voortreffelijke boek laat alle lezers op fascinerende wijze kennismaken met het wonder van . 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 vii
1 Discovery of n and Its Manifestations
1(30)
1 Prologue
1(2)
2 Discovery, Calculation, Proof
3(7)
3 Geometric Archetypes
10(2)
4 Manifestations of Archetypal Structure
12(5)
5 Geometry as a Hermeneutic Science
17(12)
6 Epilogue
29(2)
2 Pi in Mathematics and the Physical World
31(26)
1 Prologue
31(1)
2 Pythagoreanism
32(2)
3 Uniting Arithmetic and Geometry
34(5)
4 The Planetary Orbits
39(2)
5 Natural and Physical Phenomena
41(6)
6 Topology, Non-Euclidean Geometry, and Fractal Geometry
47(8)
7 Epilogue
55(2)
3 Pi in Art and Architecture
57(22)
1 Prologue
57(3)
2 Pythagoreanism in Art
60(7)
3 The Circle in Art and Symbolism
67(7)
4 Pi in Art
74(2)
5 Epilogue
76(3)
4 Pi in Popular Culture
79(23)
1 Prologue
79(2)
2 Mathematics in Popular Culture
81(10)
3 Pi in Popular Culture
91(4)
4 Pi-Mania
95(6)
5 Epilogue
101(1)
5 Order and Chaos
102(15)
1 Prologue
102(2)
2 Cohen's Dilemma
104(2)
3 Chaos Theory
106(3)
4 Order and Chaos
109(4)
5 Epilogue
113(1)
6 Final Remarks
114(3)
References 117(14)
Index 131
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.