The Geometrical Beauty of Plants
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. Ne
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The Geometrical Beauty of Plants
The Geometrical Beauty of Plants
Johan Gielis
The Geometrical Beauty of Plants
Johan Gielis Department of Biosciences Engineering University of Antwerp Antwerp Belgium
ISBN 978-94-6239-150-5 DOI 10.2991/978-94-6239-151-2
ISBN 978-94-6239-151-2
(eBook)
Library of Congress Control Number: 2017932536 © Atlantis Press and the author(s) 2017 This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. Printed on acid-free paper
An equation has no meaning for me if it does not express a thought of God. Ramanujan
“One must study not what is interesting and curious, but what is important and essential”. Pafnuty Lvovich Chebyshev’s advice to his students A special dedication to Walter Liese and Tom Gerats
Preface
In my study of natural shapes, more specifically of bamboo, I started using the superellipses and supercircles of Gabriel Lamé around 1994 to study the shape of certain square bamboos. The first publication was in the Belgian Bamboo Society Newsletter in 1996 followed by a presentation by Prof. Freddy Van Oystaeyen in the same year at a meeting at the University of Louvain organized by the Belgian Plant and Tissue Culture Group and published in the journal Botanica Scripta Belgica. Three years later, in 1997, I was able to generalize these curves into what I originally called superformula, as a generalization of supercircles, following joint work with Bert Beirinckx on superellipses. In 1999, I founded a company with the explicit aim to disseminate these ideas in science, technology, and education, with better than expected results. My first presentation on the more general use of Lamé curves in botany was in 1997 at the Symposium Morphology, Anatomy and Systematics in Leuven, in honor of the great German plant scientist Wilhelm Troll. The symposium was co-organized by the Deutsche Botanische Gesellschaft and by the Botany Department of the University of Louvain. The talk went quite well, and in the closing speech, Erik Smets remarked that it was hoped that I could bring fresh ideas to mathematical botany; the untimely death of the late Aristid Lindenmayer had left a deep gap in that field. On advice of Focko Weberling, one of Troll’s students, I was contacted by Springer Verlag that same week to publish a book on my work. In a sense, this book is 20 years overdue, but pauca sed matura was Gauss’ motto. In 2003, the first major scientific paper was published in the American Journal of Botany, on invitation by the editor in chief, Karl J. Niklas. The title “A generic geometric transformation which unifies a wide range of natural and abstract shapes” expresses the gist of the matter. This publication attracted a lot of attention, and I still think it was a good timing and (hoped for but unexpected) strategy for dissemination. In the same year, the Engli
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