Golden Section

Scott Olsen

Description

What was the golden secret known to Leonardo da Vinci, Kepler, Plato and the ancient magicians? Can there really be a key to nature and life itself? In this small but compact volume internationally renowned divine proportion supersleuth Dr Olsen unravels perhaps the greatest mystery of all time, a code that seems to underly life, the universe and everything, a pattern we instinctively recognise as beautiful, and which nature herself uses at every scale. Designed for artists and scientists alike, this is the smallest, densest and most beautiful book on the golden section ever produced. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Sujets

• History of art

Informations

• Publié par: Wooden Books
• Date de parution: 01 avril 2018
• Nombre de lectures: 4
• EAN13: 9781912706013
• Langue: English
• Poids de l'ouvrage: 14 Mo

Extrait

Vitruvian Man (Harding)
First published 2006
eBook edition © Wooden Books Ltd 2018
Published by Wooden Books Ltd.
Glastonbury, Somerset.
British Library Cataloguing in Publication Data
Olsen, S.
The Golden Section
A CIP catalogue record for this book may be obtained from the British Library.
eBook ISBN: 978-1-912706-01-3
Physical ISBN: 978-1-904263-47-0
All rights reserved.
For permission to reproduce any part of this golden little book please contact the publishers.
Designed and typeset in Glastonbury, UK
.
Converted and optimised for digital display by CPI Anthony Rowe, Chippenham, UK.
THE GOLDEN
SECTION
NATURE'S GREATEST SECRET
Scott Olsen
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; Kairos-foundation 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 Gaffurio's 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
Plato’s 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 Philosopher’s Stone
50
Appendices I: Phi Equations, and II: Fibonacci Formulæ
52
Appendix III: The Indefinite Dyad
54
Appendix IV: Designer’s Rectangles
56
Appendix V: Golden Physics
57
Appendices VI: More Lucas Magic, and VII: Phyllotaxis Angles
58

Introduction
Nature holds a great mystery, zealously guarded by her custodians from those who would profane or abuse the wisdom. Periodically portions of this tradition are quietly revealed to those of humanity who have attuned their eyes to see and ears to hear. The primary requirements are openness, sensitivity, enthusiasm, and an earnestness to understand the deeper meaning of nature’s marvels exhibited to us daily. Many of us tend to walk through life half asleep, at times numbed, if not actually deadened to the exquisite order that surrounds us. But a trail of clues has been preserved.
The secretive tradition centres on a study of number, harmony, geometry and cosmology that stretches back through the mists of time into the Egyptian, Babylonian, Indian and Chinese cultures. It is evident in the layout and relationships of the stone circles and underground chambers of ancient Europe, as well as in Neolithic stones discovered in Britain, fashioned in the form of the five regular solids. There are further clues in Maya and other Mesoamerican artifacts and buildings, and across the ocean the Gothic masons embedded it in their cathedral designs.
The great Pythagorean philosopher, Plato, in his writings and oral teachings, hinted, though enigmatically, that there was a golden key unifying these mysteries.
Here is my promise to you: if you are willing to proceed step by step through this compact little book, it will be well nigh impossible not to grasp by the end a satisfying and stunning glimpse, if not deeply provocative insight, into Nature’s Greatest Secret.
1
The Mystery of Phi
the golden thread of perennial wisdom
The history of the golden section is difficult to unravel. Despite its use in ancient Egypt and the Pythagorean tradition, the first definition we have comes from Euclid [325–265 BC] , who defines it as the division of a line in extreme and mean ratio. The earliest known treatise on the subject is Divina Proportione by Luca Pacioli [1445–1517], the monk drunk on beauty, and illustrated by Leonardo Da Vinci, who according to tradition coined the term sectio aurea , or ‘golden section’. However, the first published use of the phrase occurs in Martin Ohm’s 1835 Pure Elementary Mathematics .
There are many names for this mysterious section. It is variously called a golden or divine ratio, mean, proportion, number, section or cut. In mathematical notation it goes by the symbol t , “ tau ,” meaning “the cut,” or more commonly @ or f , “ phi ,” the first letter of the name of the Greek sculptor Phidias, who used it in the Parthenon.
So what is this enigmatic cut, and why is there so much fascination about it? One of the eternal questions asked by philosophers concerns how the One becomes Many. What is the nature of separation, or division? Is there a way in which parts can retain a meaningful relationship to the whole?
Posing this question in allegorical terms, Plato [427–347 BC] in The Republic asks the reader to “take a line and divide it unevenly”. Under a Pythagorean oath of silence not to reveal the secrets of the mysteries, Plato posed questions in hopes of provoking an insightful response. So why does he use a line, rather than numbers? And why does he ask us to divide it unevenly?
To answer Plato, we first must understand ratio and proportion.
2