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