Beyond Measure

A Guided Tour Through Nature, Myth And Number

By: Jay Kappraff

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Paperback | 18 December 2002

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616 Pages

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22.86 x 15.88 x 3.18

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A collection of essays that stand on their own but are also loosely connected. Part I documents how numbers and geometry arise in several cultural contexts and in nature: the ancient musical scale, proportion in architecture, ancient geometry, megalithic stone circles, the hidden pavements of the Laurentian library, the shapes of the Hebrew letters, and the shapes of biological forms. The focus is on how certain numbers, such as the golden and silver means, present themselves within these systems. Part II shows how many of the same numbers and number sequences are related to the modern mathematical study of numbers, dynamical systems, chaos and fractals.

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?This book should be in the hands of many non-mathematicians and mathematicians.?

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Introduction
Acknowledgements
Permission
Essays in Geometry and Number as They Arise in Nature, Music, Architecture and Design	p. 1
The Spiral in Nature and Myth	p. 3
The Vortex of Life	p. 25
Homogeneous Coordinates	p. 52
Harmonic Law	p. 54
Logarithms and the Logarithmic Spiral	p. 87
Properties of Logarithms	p. 89
Logarithms and the Musical Scale	p. 90
The Pythagorean Comma	p. 90
Vectors	p. 91
The Projective Nature of the Musical Scale	p. 93
App. 4.A	p. 104
The Music of the Spheres	p. 109
Kepler's Ratios	p. 123
Tangrams and Amish Quilts	p. 125
Steps to creating a triangular grid of circles	p. 141
Steps to creating a square circle grid	p. 143
Linking Proportions, Architecture, and Music	p. 145
An Ancient Babylonian Method for Finding the Square Root of 2	p. 167
A Secret of Ancient Geometry	p. 169
Harmonic Means	p. 189
Projective Analysis of the Equipartition Properties of the Brunes Star	p. 192
The Hyperbolic Brunes Star	p. 195
The Hidden Pavements of the Laurentian Library	p. 213
The Sacred Cut and the Square Circle Grid	p. 232
Measure in Megalithic Britain	p. 235
App. 11.A	p. 254
The Geometry of the Stone Circles	p. 256
The Flame-hand Letters of the Hebrew Alphabet	p. 261
Concepts Described in Part I Reappear in the Context of Fractals, Chaos, Plant Growth and Other Dynamical Systems	p. 289
Self-Referential Systems	p. 291
App. 13.A	p. 306
Nature's Number System	p. 309
Euler's [gamma]-Function	p. 334
The Relation between Continued Fraction Indices and the Little End of the Stick Problem	p. 335
"Kissing" Gears	p. 337
Number: Gray Code and the Towers of Hanoi	p. 340
Converting between Binary and Gray Code	p. 357
Converting from Binary to TOH Position	p. 357
Gray Code, Sets, and Logic	p. 359
Chaos Theory: A Challenge to Predictability	p. 378
App. 17.A	p. 392
Fractals	p. 394
Chaos and Fractals	p. 417
The Golden Mean	p. 443
Generalizations of the Golden Mean - I	p. 469
Generalizations of the Golden Mean - II	p. 475
Generalizations of the Vesica Pisces	p. 502
Polygons and Chaos	p. 504
App. 23.A	p. 517
App. 23.B	p. 518
App. 23.C	p. 518
Growth of Plants: A Study in Number	p. 520
The Golden Mean and Optimal Spacing	p. 537
Dynamical Systems	p. 539
Epilogue	p. 559
Bibliography	p. 565
Index	p. 577
Table of Contents provided by Blackwell. All Rights Reserved.

Beyond Measure

A Guided Tour Through Nature, Myth And Number

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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