© 2017

The Geometrical Beauty of Plants


Table of contents

  1. Front Matter
    Pages i-xxv
  2. Πρóτᾰσις—Propositio

    1. Front Matter
      Pages 1-1
    2. Johan Gielis
      Pages 3-5
  3. Eκθεσις—Expositio

    1. Front Matter
      Pages 21-21
    2. Johan Gielis
      Pages 43-55
  4. Διορισμός—Determinatio

    1. Front Matter
      Pages 85-85
    2. Johan Gielis
      Pages 87-108
  5. Κατασκευή—Constructio

    1. Front Matter
      Pages 125-125
    2. Johan Gielis
      Pages 127-144
    3. Johan Gielis
      Pages 145-166
  6. Απόδειξις—Demonstratio

    1. Front Matter
      Pages 167-167
    2. Johan Gielis
      Pages 169-185
    3. Johan Gielis
      Pages 187-203
  7. Συμπέρασμα—Conclusio

    1. Front Matter
      Pages 205-205
  8. Back Matter
    Pages 219-229

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.


Fractals Gielis Transformations Knots and Links Phyllotaxy Plant Development

Authors and affiliations

  1. 1.Department of Biosciences EngineeringUniversity of AntwerpAntwerpBelgium

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“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)​