Research Catalog

Title

The curves of life : being an account of spiral formations and their application to growth in nature, to science, and to art : with special reference to the manuscripts of Leonardo da Vinci / by Theodore Andrea Cook.

Author

Cook, Theodore Andrea, 1867-1928.

Publication

New York : Dover Publications, 1979.

Items in the Library & Off-site

Details

Description

xxx, 479 pages : illustrations; 22 cm

Summary

"Absolute uniformity of atoms and of forces," wrote Alfred R. Wallace, Darwin's fellow theorist of evolution, "would probably have led to the production of straight lines, true circles, or other closed curves. Inequality starts curves, and when growth is diverted from the direct path it almost necessarily leads to the production of that most beautiful of curves - the spiral." The open-ended curve of the spiral gives a sensation of continuous motion - of life, in fact. In The Curves of Life, Sir Theodore A. Cook (1867-1928), English author and editor, finds that the spiral or helix may lie at the core of life's first principle - that of growth. The spiral is fundamental to the structure of plants, shells, and the human body; to the periodicity of atomic elements and to an animal's horns; to microscopic DNA (the double helix) and to the Andromeda nebula. The spiral is a key to understanding organic nature, and perhaps to the living creations of the human mind. The spiral's fundamental mathematical expression is ø, or 1+[square root of 2] / 2 (= 1.618), the Ration of Pheidias, or Golden Section, or the Divine Proportion, as it has been variously termed through history. It occurs repeatedly in the productions of men: Egyptian, Greek, Roman and Gothic architects knew and admired its properties; Renaissance artists incorporated it into their theories. Leonardo designed spiral staircases and studied spirals in waves and hair; consciously or unconsciously Botticelli, Hals, and Turner composed proportional to ø. The Curves of Life portrays the significance of the spiral in 426 illustrations, from a Narwhal's tusk to Dürer's plan for a cylindrical helix. From the spiral in nature, science, and art, the author suggests ideas on the essence of beauty and man's response to it. "One of the chief beauties of the spiral as an imaginative conception is that it is always growing, yet never covering the same ground, so that it is not merely an explanation of the past, but is also a prophecy of the future."--Back cover.

Subject

• Spirals
• Morphology
• Growth
• Spirals in art
• Growth
• growth
• Spiralen
• Natuur
• Kunst

Note

• Includes index.

Contents

1. Introductory : the spiral -- 2. Mathematical definitions -- 3. Upright spirals in shells -- 4. Flat spirals in shells -- 5. Botany : the meaning of spiral leaf arrangements -- 6. Special phenomena in connection with spiral phyllotaxis -- 7. Right-hand and left-hand spiral growth effects in plants -- 8. Right-hand and left-hand spiral growth effects in plants, continued : dead tissues and spinning seeds -- 9. Right-hand and left-hand spiral growth effects in plants, continued : some special cases -- 10. Right-hand and left-hand spirals in shells -- 11. Climbing plants -- 12. The spirals of horns -- 13. Spiral formations in the human body -- 14. Right and left-handed men -- 15. Artificial and conventional spirals -- 16. The development of the spiral staircase -- 17. Spirals in nature and art -- 18. The open staircase of Blois -- 19. Some principles of growth and beauty -- 20. Final results -- Appendix. I. Nature and mathematics ; II. The [phi] progression / by William Schooling ; III. Infinite series and the theory of grouping ; IV. Origins of a symbol ; V. The spiral in pavement-toothed sharks and rays / by R. Lydekker ; The spiral in bivalve shells / by R. Lydekker ; The shell of Tranvancore ; The growth of shells ; The [phi] progression in art and anatomy.

ISBN

• 048623701X
• 9780486237015

LCCN

78014678

OCLC

• ocm04983617
• 4983617
• SCSB-14353661

Owning Institutions

Princeton University Library