The Geometrical Beauty of Plants

Part I. Πρóτᾰσις—Propositio

1. Universal Natural Shapes
Johan Gielis

2. Towards a Geometrical Theory of Morphogenesis
Johan Gielis

Part II. Eκθεσις—Expositio

3. −1, −2, −3……, Understand the Legacy
Johan Gielis

4. Lamé Curves and Surfaces
Johan Gielis

5. Gielis Curves, Surfaces and Transformations
Johan Gielis

Part III. Διορισμός—Determinatio

6. Pythagorean-Compact
Johan Gielis

7. Generalized Intrinsic and Extrinsic Lengths in Submanifolds
Johan Gielis

Part IV. Κατασκευή—Constructio

8. (Meta)Harmony
Johan Gielis

9. Natural Curvature Conditions
Johan Gielis

Part V. Απόδειξις—Demonstratio

10. Bamboo Leaves and Tree Rings
Johan Gielis

11. Snowflakes and Asclepiads
Johan Gielis

Part VI. Συμπέρασμα—Conclusio

12. The Pythagorean Theorem for the Third Millenium
Johan Gielis

Keywords: Life Sciences, Plant Sciences, Mathematical Applications in the Physical Sciences, Computer Graphics