Natural Curvature Conditions

Abstract

Curvature, in all of its aspects is at the core of geometry. Going straight is central to geometry, but it is also a fiction, since we live in a curved world with gravitational attraction in landscapes of mountains, valleys and planes. Nevertheless it is a very useful fiction, and the basis of Euclidean geometry and our science. How then to define being curved, intrinsically and/or as a deviation from planarity? This is one of the central questions in mathematics and geometry; we have derived Euclidean geometry, one geometry that is in accordance with our intuition and our position on earth (with its gravitational field).

What astonishes and bewilders me most is the scale on which Nature uses the Superformula. The search for mathematical formulas that can describe biological forms is an old one. The Gielis Formula makes it possible to describe an almost unimaginable number of natural shapes in a very simple way. One of the next challenges will be to analyze which mechanism allows organisms to use this formula for shaping its organs and bodies. And especially what we can learn from it. I am convinced that the use of this formula will also lead to an avalanche of technological breakthroughs and practical applications.

Tom Gerats