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My first novel, Love Me Back, was published on September 16. Writing the book took seven years, and along the way three chapters were published in... Continue »
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The Elements of Dynamic Symmetry

by

The Elements of Dynamic Symmetry Cover

 

Synopses & Reviews

Publisher Comments:

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 covers fundamental rectangles while Part II explains compound rectangles, many of which were taken from or suggested by the analysis of Greek art objects. 118 illustrations.

Synopsis:

Controversial but lasting thesis that design and great art can be created by application of easily followed mathematics. 118 illustrations.

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

Product Details

ISBN:
9780486217765
Author:
Hambidge, Jay
Publisher:
Dover Publications
Author:
Art Instruction
Subject:
Techniques
Subject:
Design
Subject:
Design - General
Subject:
Art, greek
Subject:
Techniques - General
Subject:
Art-Miscellaneous Techniques
Copyright:
Edition Description:
Trade Paper
Series:
Dover Art Instruction
Publication Date:
19670631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
174
Dimensions:
8.5 x 5.38 in 0.56 lb

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"Synopsis" by ,
Controversial but lasting thesis that design and great art can be created by application of easily followed mathematics. 118 illustrations.

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