Knots and Everything

A Guided Tour Through Nature, Myth And Number

By: Jay Kappraff

Write A Review

Hardcover | 18 December 2002

At a Glance

Hardcover
616 Pages

Dimensions(cm)
22.86 x 15.88 x 3.18

Hardcover

RRP $156.99

$141.75

10%OFF

or 4 interest-free payments of $35.44 with

Ships in 15 to 25 business days

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.

Industry Reviews

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

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Arts & Entertainment Design, Industrial & Commercial Arts, Illustration Mathematics Geometry Society & Culture Cultural Studies History of Ideas Science Science in General Popular Science Medicine

Medicine in General History of Art & Design Styles History of Mathematics Booktopia Publisher Services World Scientific Publishing

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.

Knots and Everything

A Guided Tour Through Nature, Myth And Number

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Mathematics

Mathematics for Technicians

7th Edition

The Infinite Game

From the bestselling author of Start With Why

Nelson Senior Maths 11 Mathematics Essential Student Book with 1 Access Code for the Australian Curriculum

Primary Mathematics

4th Edition - Integrating Theory with Practice

The Art of Gathering

How We Meet and Why It Matters

How to Win At Chess

The Ultimate Guide for Beginners and Beyond

Oxford Maths for Australian Schools Year 3 Value Pack

3rd Edition

Oxford Maths for Australian Schools Year 4 Value Pack

3rd Edition

Oxford Maths for Australian Schools Year 6 Value Pack

3rd Edition

Maths in Focus 11 Mathematics Advanced Student Book with Nelson MindTap

The Science of Scaling

Using Data to Decide When -- and How Fast -- to Scale Revenue

Collins Classics - The Republic

Collins Classics

Nelson Senior Maths 12 Mathematics Essential Student Book + 1 Code Access Card for Western Australia and Australian Curriculum

Nelson WAmaths Mathematics Applications

11th Edition

Oxford Maths for Australian Schools Value Pack Year 5

Oxford Maths

Maths in Focus 11 Mathematics Standard (Pathway 2) Student Book with Nelson MindTap

Calculus

12th Edition- Early Transcendentals, International Adaptation

Kumon Grades 6-8 Algebra

Algebra

In All Likelihood

Statistical Modelling and Inference Using Likelihood

The Laws of Thought

The Quest for a Mathematical Theory of the Mind

Oxford Maths for Australian Schools Year 5 Practice and Mastery Book

3rd Edition

Oxford Maths for Australian Schools Year 2 Value Pack

3rd Edition

Deleuze, Mathematics, Metaphysics

Difference and Necessity

Undergraduate Lecture Notes in Physics

A Practical Guide with Problems and Solutions

This product is categorised by