Beyond measure : a guided tour through nature, myth, and number / Jay Kappraff.

Format:

Book

Author/Creator:

Kappraff, Jay.

Series:

K & E series on knots and everything ; v. 28.

K & E series on knots and everything ; v. 28

Language:

English

Subjects (All):

Geometry.

Mathematics.

Design.

Physical Description:

1 online resource (620 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

This book consists 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

Contents:

Contents ; Introduction ; Acknowledgements ; Permission ; Part I Essays in Geometry and Number as They Arise in Nature Music Architecture and Design ; Chapter 1 The Spiral in Nature and Myth ; 1.1 Introduction ; 1.2 The Australian Aborigines ; 1.3 The Fali

1.4 The Precession of the Equinoxes in Astronomy and Myth 1.5 Spiral Forms in Water ; 1.6 Meanders ; 1.7 Wave Movement ; 1.8 Vortices and Vortex Trains ; 1.9 Vortex Rings ; 1.10 Three Characteristic Features of Water ; 1.11 The Flowform Method ; 1.12 Conclusion

Chapter 2 The Vortex of Life 2.1 Introduction ; 2.2 Projective Geometry ; 2.3 Perspective Transformations on the Line to Points on a Line ; 2.4 Projective Transformations of Points on a Line to Points on a Line ; 2.5 Growth Measures ; 2.6 Involutions ; 2.7 Circling Measures

2.8 Path Curves 2.9 Path Curves in Three Dimensions ; 2.10 Field of Form ; 2.11 Comparison of Three Systems ; 2.12 Conclusion ; Appendix 2.A Homogeneous Coordinates ; Chapter 3 Harmonic Law ; 3.1 Introduction ; 3.2 Musical Roots of Ancient Sumeria ; 3.3 Musical Fundamentals

3.4 Spiral Fifths 3.5 Just Tuning ; 3.6 Music and Myth ; 3.7 Musically Encoded Dialogues of Plato ; 3.8 The Mathematical Structure of the Tonal Matrix ; 3.9 The Color Wheel ; 3.10 Conclusion ; Appendix 3.A ; 3.A.1 Logarithms and the Logarithmic Spiral

3.A.2 Properties of Logarithms

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 565-576) and index.

ISBN:

9789812778444

9812778446

OCLC:

879023686