Spirals: From Theodorus to Chaos

Contents
Acknowledgements ix
Part I: The Hedrick Lectures 1
Foreword to The Hedrick Lectures 3
Lecture I: What is a Spiral? Spirals Old and New 7
Lecture II: Lessons from Euler's Ghost 33
Lecture III: Theodorus Goes Wild 45
Part II: Technical Developments 65
Supplement A: The Spiral of Theodoras, Special
Functions, and Numerical Analysis.
By Walter Gautschi 67
Supplement B: The Dynamics of the Theodoras Spiral.
By Arieh Iserles 89
Part III: Historical Supplements 127
Foreword to Historical Supplements 129
A. Plato: From Timaeus 131
B. Plato: Prom Theaetetus 133
C. Archimedes: Prom Peri Elikon 137
D. Evangelista Torricelli: Prom De Infinitis Spiralibus 143
E. Jean Bernoulli: Prom Opera Omnia 147
F. James Joseph Sylvester: Prom Note on the Successive
Involutes of a Circle 149
G. Henri Poincare: Prom Memoire sur les Courbes 153
H. Edmund Hlawka: Prom Gleichverteilung und
Quadratwurzelschnecke 157
Epilogue 169
Bibliography 181
Notes 193
Index 233