Minkowski Geometry in the Mathematical Modeling of Natural Phenomena

The samples of geometric interpretation of space-time features of special relativity theory and phyllotaxis botanic phenomenon demonstrate variance of Minkovski’s theory application in mathematic modeling of natural phenomena. It is a well-known fact that in 1908, i.e. three years after A. Einstein’s theory of relativity was published, mathematician G. Minkowski made public geometric interpretation of this theory. Peculiarity of Minkowski geometry (in other words, of pseudo-Euclid geometry) lies in the fact that hyperbolic rotation becomes a typical motion of space (plane) symmetric transformation. We remind that in “usual” – Euclidean geometry – analogous symmetry motion is circular rotation. Applying pseudo-Euclidean geometry and its trigonometric tools, Minkowski exhaustively described in mathematical terms all the effects of relative mechanics. Later we’ll return to the details of this interpretation while so far it is necessary to stress that for a long time space-time physics of relativity theory was considered to be the only field where Minkowski geometry could be applied. However, the paper [1] which appeared in 1989 as well as later publications [2, 3, 4, 5] showed that Minkowski geometry was realized in growth mechanism of botany phenomenon phyllotaxis. It was an unexpected result despite the fact that it was part of Vernadski’s prediction who under influence of the theory of relativity substantiated an opinion about non-Euclid character of wildlife geometry [6]. At any rate, it became understandable that ideas about the role of Minkowski geometry in nature were not limited by space-time physics. Soon legitimacy of these ideas was confirmed by the results of mathematical successions of pattern-shaping regularities in architecture and art, in particular, by the fact of hyperplane application to illustrate artistic proportioning schemes [7]. Scientific results known nowadays that find Minkowski geometry regularities in various phenomena,