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Golden Section

4 Deep gratitude to my loving parents, Ilene Clarion Thanks to contributors Keith Critchlow, John Michell, Lance Harding, Benjamin Bryton, Garth Norman, Mark Reynolds, Robin Heath, Richard Heath, Pablo Amaringo, Zachariah Gregory, especially to my editor John Martineau. I am grateful for discussions with Dan Pedoe, David Bohm, Huston Smith, Douglas Baker, Stephen Phillips, Edgar Mitchell, David Fideler, Garileo Pedroza, Robert Powell Sr., Alexey Stakhov, Michael Baron, Bill Foss. Special thanks to my lovely wife, Pam. Thank you CFCC for the sabbatical. Further sources P. Hemenway, Divine Proportion G. Doczi, Power of Limits M.Schneider, Golden Section Workbook Kairosfoundation F worksheets M. Livio, Golden Ratio M. Ghyka, Geometry of Art Life H.E. Huntley, Divine Proportion R.A. Dunlap, The Golden Ratio. Above Francino Gaffurios early woodcut of a Liberal Arts lesson. Previous Page Lucas and Fibonacci spiral phyllotaxis showing Archimedean spiral after Bursill, Rouse Needham. conTEnTs Introduction 1 The Mystery of Phi 2 Ratio, Means Proportion 4 Platos Divided Line 6 Phi on the Plane 8 The Fibonacci Sequence 10 Phyllotaxis Patterns 12 Order Behind Diversity 14 Lucas Number Magic 16 All Creatures 18 Phi in the Human Body 20 Growth Diminution 22 Exponentials and Spirals 24 Golden Symmetry 26 Phi in Human Culture 28 Ancient of Days 30 My Cup Runneth Over 32 A Sacred Tradition 34 Phi in Painting 36 Melody Harmony 38 All That Glisters 40 The Golden Chalice 42 Golden Polyhedra 44 Phi in the Sky 46 Resonance Consciousness 48 The Philosophers Stone 50 Appendices I Phi Equations, and II Fibonacci Formul 52 Appendix III The Indefinite Dyad 54 Appendix IV Designers Rectangles 56 Appendix V Golden Physics 57 Appendices VI More Lucas Magic, and VII Phyllotaxis Angles 58
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