The Elements of Dynamic Symmetry

by Jay Hambidge

Overview

Is design intuitive or is it consciously and methodically worked out? Are there basic rules governing design that, when learned, will facilitate the creative process? These questions have been asked by artists, art historians, and art critics throughout the ages.
Convinced that design was not purely instinctive, Jay Hambidge (1867–1924) spent much of his life searching for the technical bases of design. He found his answer in dynamic symmetry, one of the most provocative and stimulating theories in art history. Hambidge's study of Greek art convinced him that the secret of the beauty of Greek design was in the conscious use of dynamic symmetry — the law of natural design based upon the symmetry of growth in man and in plants. But Hambidge, who was not only a theoretician but also a practicing artist, did much more than analyze classical art and its principles of design: he worked out a series of root rectangles that the artist, using the simple mathematics supplied in this book, can easily follow and apply in his own work.
Originally published as a series of lessons in Hambidge's magazine, The Diagonal, this engrossing book explains all the basic principles of dynamic symmetry. Part I sets forth the fundamental rectangles with their simple divisions based on the proportioning law found in nature; Part II explains compound rectangles, many of which were taken from or suggested by analysis of objects of Greek art.
Whether read for its historical importance in art theory, for its illuminating insights into Greek art, or for its practical value to today's artists and commercial designers, The Elements of Dynamic Symmetry has much to offer anyone who is interested in the principle of design.

Product Details

ISBN-13:	9780486217765
Publisher:	Dover Publications
Publication date:	06/01/1967
Series:	Dover Art Instruction Series
Pages:	176
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

INTRODUCTION
Synthesis and analysis
The difference between static and dynamic symmetry
Sources for the study of dynamic symmetry
THE DYNAMIC SYMMETRY OF THE PLANT
The summation series
How dynamic symmetry was discovered
The logarithmic spiral
The law of phyllotaxis
Explanation of its application to design
PART I. SIMPLE RECTANGLES
LESSON 1. THE SQUARE (OR UNITY)
Methods for manipulating the plan forms of nature
The square and its diagonal
The square and the diagonal to its half
The root rectangles constructed outside a square
The linear proportions of the root rectangles
The root rectangle constructed within a square
LESSON 2. THE RECTANGLE OF THE WHIRLING SQUARES (1.618) AND THE ROOT-FIVE RECTANGLE (2.236)
Construction of a whirling square rectangle
Method for constructing a root-five from a whirling square rectangle
"Cutting a line in what Plato called "the section"
LESSON 3. THE APPLICATION OF AREAS
Simple method of the Greeks for the division of areas
Process for the application of the square on an end to a side of a rectangle
LESSON 4. THE RECIPROCAL
Definition of a reciprocal
Importance to design of a reciprocal shape
"Explanation of the name "whirling squares"
Arithmetical statement of the reciprocal considered
Relationship between whirling square reciprocals and the root-five rectangle
LESSON 5. THE DIAGONAL
The diagonal of a rectangle
The 47th proposition of the first book of Euclid
The diagonal of a reciprocal
Various methods for establishing reciprocals
The rectangular spiral
Intersection of a diagonal of the whole with a diagonal of the reciprocal
Division of the root rectangles into their reciprocals
LESSON 6. THE ROOT-TWO RECTANGLE (1.4142)
Why a root-two rectangle is so called
Rectangular spirals in a root-two rectangle
A root-two rectangle plus a square
A root-two rectangle described within a square
Root-two rectangles described on the four sides of a square
The reciprocal of a root-two rectangle plus a square
A square plus two root-two reciprocals
Division of a root-two rectangle into its reciprocals
Division of any rectangle into thirds
LESSON 7. THE ROOT-TWO RECTANGLE AND THE APPLICATION OF AREAS
"A square "applied" on the end of a root-two rectangle "
Application of areas to other areas
A square applied to each end of a root-two rectangle
Division of a root-two rectangle when the diagonal of the whole cuts the side of an applied square
Application of a square on an end to a side of a root-two rectangle
Similarity of figure
A root-two rectangle applied to the square of a 2.4142 shape
A square applied to a root-two reciprocal
LESSON 8. THE ROOT-THREE RECTANGLE (1.732)
Construction of a root-three rectangle
Application of a square on the end of a root-three rectangle
A square on an end applied to a side or a root-three rectangle
Division of the root-three rectangle into its reciprocals
Different ways of dividing the root-three rectangle into similar shapes
LESSON 9. THE ROOT-FOUR RECTANGLE (2.)
Construction of a root-four rectangle
Division into its reciprocals
Dynamic and static treatment of a root-four rectangle
A whirling square rectangle applied to a root-four rectangle
A square on an end applied to a side or a root-four rectangle
LESSON 10. THE ROOT-FIVE RECTANGLE (2.236)
Construction of a root-five rectangle
Four whirling square rectangles described on the four sides of a square
A square applied on the end of a root-five rectangle
A square on an end applied to a side of a root-five rectangle
Division of the root-five rectangle into its reciprocal
LESSON 11. THE SPIRAL AND OTHER CURVES OF DYNAMIC SYMMETRY
The logarithmic or constant angle spiral
The first geometrical discovery made by the Greeks
"Another great discovery, that of a mean proportional"
Definition of a mean proportional
Lines in continued proportion
Logarithmic spiral drawn within a rectangle
Construction of volutes of different kinds
LESSON 12. GENERAL CONSTRUCTIONS FOR SIMILARITY OF FIGURE
Enlargement and reduction of shapes by a diagonal
Construction of similar shapes which can be moved up or down on a medial line
Similar shapes constructed from any point in a rectangle
Properties of modulation and measurableness in dynamic areas
Properties of shapes similar to dynamic subdivisions of areas
Construction of shapes similar to dynamic subdivisions of areas.
Eternal principle of growth in dynamic shapes
PART II. COMPOUND RECTANGLES
LESSON I. THE COMPLEMENT
Form and color complements compared
Definition of a complement
Relationship between areas and their complements
Division of areas in terms of their complements
A reciprocal in a complement of a root-five rectangle
Intention the dominant factor in artistic expression
Importance to the artist of the use of diagonal lines
To transfer a complement
How to construct different rectangles in single and multiple form within areas
LESSON II. RHYTHMIC THEMES OF THE WHIRLING SQUARE RECTANGLE
Root-five rectangles within the rectangle of the whirling squares
Arithmetical analysis
Other subdivisions of the whirling square rectangle
Summing up of other ratios appearing in this lesson
LESSON III. THE SQUARE PLUS A ROOT-FIVE RECTANGLE (1.4472) AND A WHIRLING SQUARE RECTANGLE APPLIED TO A SQUARE
"The 1.4472 rectangle, the key ratio of the Parthenon plan"
Its natural source in the regular pentagon
How to draw a square plus a root-five rectangle
Connection between the ratio 1.4472 and 1.382
How a whirling square rectangle is applied to a square
Diagonals of the whole and diagonals of the reciprocals drawn to a whirling square rectangle within a square
LESSON IV. COMPOUND RECTANGLES WITHIN A SQUARE
Area in excess of a root-five rectangle placed within a square
Natural source of an .809 rectangle
A .191 rectangle
A 1.191 rectangle
LESSON V. FURTHER ANALYSIS OF THE SQUARE
Analysis of excess areas resulting from application of a whirling square rectangle to a square
LESSON VI. THE ADDITION OF UNITY TO DYNAMIC AREAS
&
"List, with corresponding diagrams, of the most important ratios of dynamic symmetry, with their reciprocals, 1/2 ratios and 1/2 reciprocals"
LESSON IX. RATIOS MOST FREQUENTLY USED?Continued
Analysis of a 2.309 shape with list of its subdivisions
"List of subdivisions of the 2.4472, 2.472, 2.618 and 2.764 shapes"
Odd compound rectangles within a square
WHAT INSTRUMENTS TO USE AND HOW TO USE THEM
DEFINITIONS SELECTED FROM THE THIRTEEN BOOKS OF EUCLID'S ELEMENTS
GLOSSARY