The book offers new sensational information on the realization of rules of the geometry of Minkovskiy in nature. It has been done for the first time after Herman Minkovskiy published his geometrical interpretation of the special theory of relativity one hundred years ago. The author investigates its realization in nature, namely in the growth mechanism of spiro-symmetrical (the so called phylotaxis) plant forms. A detailed mathematical decoding of this mechanism unexpectedly reveals the involvement of golden section - a magic number, with which the history of science and art have always associated the idea of harmony and perfection. The book contains historical information on the development of geometric ideas in science and art, on the evolution of spatial conceptions, their peculiarities and their role in the scientific outlook of the 20th century. The process of the change of spatial conception and, accordingly, of methodological approaches in the architecture and design of the 20th century are regarded from special "geometric" positions.