The ISSBG 2022 symposium brought together botanists, biologists, technologists, physicists, applied mathematicians and geometers. Contributions spanned a wide range of subjects, but the common themes were:
The name of the symposium symbolizes the close connection between geometry and the natural sciences.
Geometree comes from a wonderful book – The Poetry of the Universe – by Robert Osserman: “We may picture the product of three thousand years of geometric inventiveness in the form of a tree – the “Geometree” – whose roots go back even further and whose branches represent the outcome of centuries of discovery and creation. With or without application, the branches and fruits of this tree are worth contemplating as a remarkable product of human imagination. The Geometree is healthy, vigorous and in full foliage, older than any redwood, and fully as majestic. ”
Square bamboos opened the door to a uniform and unified mathematical description of natural shapes. In 1993, superellipses were first used to describe the culm cross-sections of square bamboos (Chimonobambusa species) and other square shapes in botany. Starfish and many other natural shapes with different symmetries followed soon, through the generalization of Lamé curves to Gielis Transformations (also known as the “Superformula”), as a uniform description of natural shapes and phenomena.
The ISSBG 2022 symposium was divided into three sessions: (1) Geometry; (2) Mathematics; (3) Applications in Biology and Technology. Contributions in Geometry deal with position vectors in submanifold theory, the construction of equilibrium surfaces with symmetry for anisotropic energy functions, Generalized Möbius-Listing bodies and geometric algebra using R-functions. Contributions in Mathematics deal with using nested analytic functions to compute Laplace Transforms, the stability of solutions in mixed differential equations and Umbral calculus. Applications in technology involve computational optimization of antennas, applications of superformula in CAD/CAM and technology, modeling of animal bones using superellipses and the connection to complexity theory.