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The Geometrical Beauty of Plants

  • Book
  • © 2017

Overview

Authors:
  1. Johan Gielis

    1. Department of Biosciences Engineering, University of Antwerp, Antwerp, Belgium

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  • Step-by-step explanation of Gielis curves, surfaces and transformations and their properties
  • The book provides new insights in the relationship between botany and mathematics
  • The book illustrates the emergence of beauty and harmony from mathematics
  • The book bridges the gap between (differential) geometry and algebra
  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxv
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  2. Πρóτᾰσις—Propositio

    1. Front Matter

      Pages 1-1
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    2. Universal Natural Shapes

      • Johan Gielis
      Pages 3-5

    3. Towards a Geometrical Theory of Morphogenesis

      • Johan Gielis
      Pages 7-20

  3. Eκθεσις—Expositio

    1. Front Matter

      Pages 21-21
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    2. −1, −2, −3……, Understand the Legacy

      • Johan Gielis
      Pages 23-41

    3. Lamé Curves and Surfaces

      • Johan Gielis
      Pages 43-55

    4. Gielis Curves, Surfaces and Transformations

      • Johan Gielis
      Pages 57-83

  4. Διορισμός—Determinatio

    1. Front Matter

      Pages 85-85
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    2. Pythagorean-Compact

      • Johan Gielis
      Pages 87-108

    3. Generalized Intrinsic and Extrinsic Lengths in Submanifolds

      • Johan Gielis
      Pages 109-123

  5. Κατασκευή—Constructio

    1. Front Matter

      Pages 125-125
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    2. (Meta)Harmony

      • Johan Gielis
      Pages 127-144

    3. Natural Curvature Conditions

      • Johan Gielis
      Pages 145-166

  6. Απόδειξις—Demonstratio

    1. Front Matter

      Pages 167-167
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    2. Bamboo Leaves and Tree Rings

      • Johan Gielis
      Pages 169-185

    3. Snowflakes and Asclepiads

      • Johan Gielis
      Pages 187-203

  7. Συμπέρασμα—Conclusio

    1. Front Matter

      Pages 205-205
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    2. The Pythagorean Theorem for the Third Millenium

      • Johan Gielis
      Pages 207-217

  8. Back Matter

    Pages 219-229
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Keywords

About this book

This book focuses on the origin of the Gielis curves, surfaces and transformations in the plant sciences. It is shown how these transformations, as a generalization of the Pythagorean Theorem, play an essential role in plant morphology and development. New insights show how plants can be understood as developing mathematical equations, which opens the possibility of directly solving analytically any boundary value problems (stress, diffusion, vibration...) . The book illustrates how form, development and evolution of plants unveil as a musical symphony. The reader will gain insight in how the methods are applicable in many divers scientific and technological fields.

Reviews

“The book is a monograph describing his research into the mathematical principles underlying plant morphology originally prompted by his study of the cross-sectional shapes of bamboo stems. … This book should be of interest to anyone who works in biological morphology because it describes a quantitative way of describing biological shapes.” (Computing Reviews, March, 2018)​

Authors and Affiliations

  • Department of Biosciences Engineering, University of Antwerp, Antwerp, Belgium

    Johan Gielis

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