Gielis J. The Geometrical Beauty of Plants

Atlantis Press, 2017. — 235 p. — ISBN: 978-94-6239-150-5.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.Universal Natural Shapes
Towards a Geometrical Theory of Morphogenesis
−1, −2, −3... Understand the Legacy
Lamé Curves and Surfaces
Gielis Curves, Surfaces and Transformations
Pythagorean-Compact
Generalized Intrinsic and Extrinsic Lengths in Submanifolds
(Meta)Harmony
Natural Curvature Conditions
Bamboo Leaves and Tree Rings
Snowflakes and Asclepiads
The Pythagorean Theorem for the Third Millenium