The Curves of Life

by Theodore A. Cook

Overview

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 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."
Martin Gardner, mathematician and author, said of The Curves of Life, "This is the classic reference on how the golden ratio applies to spirals and helices in nature."

Product Details

ISBN-13:	9780486237015
Publisher:	Dover Publications
Publication date:	02/01/1979
Series:	Dover Books Explaining Science Series
Edition description:	Revised ed.
Pages:	528
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

CHAPTER I INTRODUCTORY-THE SPIRAL
Growth and Beauty and Spiral Formations
Letters from Sir E. Ray Lankester and Dr. A. R. Wallace
Measurement of Bones
Nature not mathematically exact
Gravity and Perfect Motion: Spirals and Perfect Growth
"Spirals in Shells, Whirlwinds, Human Organs, Nebulæ, etc."
"Classification, Utility, and Antiquity of Spirals"
Need of Theory
CHAPTER II MATHEMATICAL DEFINITIONS
Spiral Appearances subjective
Flat Spirals
Left Hand and Right Hand
Conical and Cylindrical
Ionic Volute drawn by means of a Shell
Ways of making Spirals
Curious Nomenclature used by Botanists
CHAPTER III UPRIGHT SPIRALS IN SHELLS
Formation of Spirals in Shells
Tube coiled round Axis
Life History of a Series in One Shell
Acceleration and Retardation
Natural Selection
Adjustment to Environment
Survival and Spiral Variation
Right-hand and Life-hand Shells
Ammonite and Nautilus
External and Internal Spirals
Supporting the Central Column
Comparison with Insects and Plants
Multiple Spirals
CHAPTER IV FLAT SPIRALS IN SHELLS
Nautilus and Logarithmic Spiral
Equiangular Spiral a Manifestation of Energy
Deviation from Cuve of Perfect Growth
Leonardo da Vinci as Student of Shells
Work of Professor Goodsir
Varying Inversely as the Cube and the Square
Significance of the Position of the Siphuncle
Verticle and Horizontal Views of Shells and Plants
CHAPTER V BOTANY-THE MEANING OF SPIRAL LEAF ARRANGEMENTS
Provision for Air and Sunlight
Overlapping of Old Leaves by Young
Advantages of Overlapping in Intense Glare
Spiral Plan for Minimum Overlap
The Ideal Angle
Fibonacci Series
Mr. A. H. Church on Logarithmic Spirals in Phyllotaxis
CHAPTER VI SPECIAL PHENOMENA IN CONNECTION WITH SPIRAL PHYLLOTAXIS
The Sprial Theory of Schimper
Growing Systems in place of Adult Construction
A Logarithmic Spiral on a Plane Surface
The Fibonacci Series again
Radial Growth and Spiral Patterns
A Standard for Comparison
Examples of Different Systems
CHAPTER VII RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANTS
Twist Effects:
(i.) Spiral Leaf Arrangements
(ii.) Overlapping Effects
(iii.) Unequal Growth in Main Axis
(iv.) Spiral Movement of Growing Ends
(v.) Spiral Growth of Twining Plants
(vi.) Spiral Effects after Death
Nomenclature of Spirals
Numerical Proportions of Right and Left Hand
CHAPTER VIII RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANTS (continued) DEAD TISSUES AND SPINNING SEEDS
Spiral Twisting of Dead Tissues
Coiling when Drying: Straightening when Wet
Predominace of Right-hand Fibres
Seed Spinning in Flight
The Mechaanism of Winged Fruits
CHAPTER IX RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANS (continued) SOME SPECIAL CASES
Anomalous Variation producing Spirals
"Spiral Staircase" Construction"
Peculiarities of Spiral Spermatozoids
Male Cells of Cycads and Chinese Maidenhair Tree
Spirals and Locomotion
Prevalance of Right-hand and Left-hand Spirals
CHAPTER X RIGHT-HAND AND LEFT-HAND SPIRALS IN SHELLS
Contrast of Trees with Shells
Spiral Fossils in Nebraska
Determination of Hand in Shells
Different Hand in Fossils and Survivors of same Species
Left-hand Spirals of Tusks
"Sinistral Shell, but Dextral Animal"
Shells among Primitive Peoples
Following the Sun
The Swastika
Spiral Formation and the Prinicple of Life
CHAPTER XI CLIMBING PLANTS
The Purpose of Climbing
With and Without Tendrils
Hand and Species
Mr. G. A. B. Dewar on Climbers
"Feeling" for Supports "
Inheritance and Memory
Circumnutating
"Sense Organs" for Gravity and Light"
The Statolith Theory
Influence of Light and Moisture
Effects of Climate Reversal of Spirals
CHAPTER XII THE SPIRALS OF HORNS
Pairs of Horns
Odd-toed and Even-toed Hoofed Animals
The Angle of the Axis in Horns
Suggested Geometrical Classification
Distinctions between Horns of Wild Animals and Tame
Homonymous Horns
"Perversion" and Heteronymous Horns"
"Comparison with other Spiral Growths, as of Plants and Shells"
Exceptions to Dr. Wherry's Rule
Tame Animals showing Twists of their Wild Ancestors
Development or Degeneration?
The Problem stated
CHAPTER XIII SPIRAL FORMATIONS IN THE HUMAN BODY
Natural Objects do not consciously produce Spirals
Deviation from Mechanical Accuracy
Spiral Formations of Upper End of Thigh Bone
Growth and Change
Corresponding Structures in Birds and Mammals
Conical Spiral of Cochlea
"Spiral Formations: Umbilical Cord, Skin, Muscular Fibres of Heart, Tendo Achillis, The Humerus (Torsion), Ribs, Joints, Wings and Feathers, Eggs, Animalculæ"
CHAPTER XIV RIGHT AND LEFT-HANDED MEN
Right and Left-handedness
Legs and Arms of Babies
Leonardo da Vinci
Preference of Orientals for Left-hand Spirals
Prehistoric Man generally Right-handed
Skill of Left-handed Men: Examples from the Bible
The Hand of Torques
The Rule of the Road
"Left-handed Sportsmen: Anglers, Archers, etc."
Left-handed Artists
More about Leonardo
Letter from Mr. A. E. Crawley
CHAPTER XV ARTIFICIAL AND CONVENTIONAL SPIRALS
Spiral Decoration in Prehistoric Times
The Successive Races of Man
Artistic Skill of Aurignacians
Magdalenian Civilisation
The Spiral as a Link between Aurignacians and Greeks
The Mycenaean and Minoan Age
Late Neolithic Ornamentation
Distribution of Spirals in United Kingdom
Scandinavia and Ireland
Egyptian Spiral in Danish Celts
Neolithic Stones and Etruscan Vases
The Sacred Lotus
"The "Unlucky" Swastika"
Spirals in Greek Art
Origin of the Volute
Theory and Experiment
The Iron Age
Uncivilised Communities of the Present Day
Mediæval Gothic
Violin Heads
"Cylindrical Spirals: Torques, Armlets, "Collars"
CHAPTER XVI THE DEVELOPMENT OF THE SPIRAL STAIRCASE
Spiral Columns
Rarity of Left-hand Spirals
Right-handed Architects and Workmen
Accidental Cause of a Twisted Spire
Efficiency and Beauty
Practical Origin of Spiral Staircases
Gradual Evolution
Central Support
The Hand Rail
Defence against Attack
Double Spiral Staircases
CHAPTER XVII SPIRALS IN NATURE AND ART
Shells and Spiral Staircases
Practical Problems and Beauty of Design
Efficiency and Beauty
Leaning Companiles Intentionally Designed
Charm of Irregularity
The Parthenon
Architecture and Life
Quality of Variation in Greek Architecture
Expression of Emotions
Artistic Selection from Nature
CHAPTER XVIII THE OPEN STAIRCASE OF BLOIS
The Staircase designed by Leonardo da Vinci
Voluta Vespertilo
The King's Architect
A Left-handed Man
Work of Italians in France
Leonardo's Manuscripts
His Theories of Art
CHAPTER XIX SOM
"Dürer and the "Cavallo"
Dürer's Mathematical Studies
"Dante, Leonardo, Goethe"
The Experimental Method
"Beauty is "Fitness Expressed"
The Value of Delicate Variations
"Good Taste"
Processes of Scientific Thought
CHAPTER XX FINAL RESULTS
The Logarithmic Spiral as an Abstract Conception of Perfect Growth
Spiral Nebulæ
Dr. Johnstone Stone's Spiral of the Elements
Infinite Series and the Rhythmic Beat
Phyllotaxis
The Ratio of Pheidias
The F Spiral
Space Proportion
Art and Anatomy
The Theory of Exceptions
"Value of a "Law"
Complexities of the Higher Organism
"A Flame to Curiosity"
The Methods of Science
APPENDIX
I. Nature and Mathematics (illustrated)
II. The F Progression. By William Schooling
III. Infinite Series and the Theory of Grouping
IV. Origins of a Symbol (illustrated)
V. The Spiral in Pavement-toothed Sharks and Rays (illustrated). By R. Lydekker
VI. The Spiral in Bivalve Shells (illustrated). By R. Lydekker
VII. The Shell of Travancore
VIII. The Growth of Shells (illustrated)
IX. The F Progression in Art and Anatomy (illustrated)