GEOMETRY. WHAT ELSE !? - MORE OF “ENVIRONMENTAL GEOMETRY”

Abstract

This paper is an addendum to a previous article [01] in which several examples demonstrate that “all natural or artificial objects have a shape or form resulting from a natural (bio-physical) or technical (design) process, and therefore have an intrinsic (immanent) geometric constituent”, focusing on the fact that “reality reveals geometry and geometry creates reality”. Since many objects are metaphors for geometric and mathematical content and the starting point for mathematical abstraction, one can conclude that geometry is simply everywhere. This sort of “Appendix” focuses on the symbiotic terms “grasping via senses” and “meaning” in connection with geometry and its visualisation and interpretation, from objects found in our usual environment. A real object that we see or recognize may even gain spiritual meaning, because it is extraordinary and rare and has, therefore, besides its somehow practical purpose, a symbolic one. Here, simplicity, symmetry, smoothness and regularity play an essential role beyond simple aesthetics. In our mainly secular culture, the aesthetic point of view stands in the foreground. KEYWORDS: elementary geometry, intuitive geometry, right angle, cross and square, proofs without words.