Elements of Dynamic Symmetry

Overview

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.

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The Elements of Dynamic Symmetry

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Overview

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.

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Product Details

  • ISBN-13: 9780486217765
  • Publisher: Dover Publications
  • Publication date: 6/1/1967
  • Series: Dover Art Instruction Series
  • Pages: 133
  • Sales rank: 336,144
  • Product dimensions: 5.68 (w) x 8.24 (h) x 0.52 (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

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