Аннотация

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. Thus, the central point of the book is a scientific discovery, which concerns the most general laws of nature and testifies to the fundamental ties between different trends in scientific perception which seem to have long ago and forever lost such ties. In this context A. Einstein, V.I.Vernadsluy and Le Corbusier have been mentioned.

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 20^th century.

The process of the change of spatial conception and, accordingly, of methodological approaches in the architecture and design of the 20* century are regarded from special "geometric" positions.

The book covers a large number of topics and aspects, but the main idea running all through it is the idea of interaction and mutual development of science and art.

For architects, designers, art critics, as well as for mathematicians, biologists, physicists, philosophers.

Contents
Preface			6
Проблема геометричних просторових уявлень у мистецтвознавстві			10
Chapter 1. Genesis of geometrical knowledge in historical development of art			15
1.1	Souses of tradition of geometry in art		17
1.2	Development of geometry on the basis of methodological problems of art		29
	1.2.1	Golden section	29
	1.2.2	Analysis of concepts of the theory of proportions	41
	1.2.3	Historical forming of ideas about space and word. Classic concept of the space	55
Chapter 2. The development of geometrical ideas and conceptions in modern science and art			65
2.1	Concept "space-time"		67
	2.1.1	Change of geometrical ideas in physics in XX century	67
	2.1.2	"Space-time" as problem of natural science	73
	2.1.3	New concept of space in the theory of art	77
2.2	Reorientation of geometrical theories in modern theory and methodology of creation of forms		82
	2.2.1	Geometry in creative practice of design and architecture	83
	2.2.2	Geometry in studies of art. Principle of symmetry	94
	2.2.3	Dynamism and dynamic creation of forms	108
	2.2.4	Geometry of nature structures as actual problem of the theory methodology of creation of forms	114
Chapter 3. Geometry of hyperbola - universal regularity of nature and art			123
3.1	Geometry of phylotaxis		127
	3.1.1	Structural and numeral peculiarities of phylotaxis	127
	3.1.2	Dynamic symmetry	132
	3.1.3	Analytically-geometrical investigations	141
3.2	Interpretation of spatial models of phylotaxis		155
3.3	The geometry of Minkovskiy as regularity of artistic creativity		180
Conclusion			183
Afterward Golden section and Non-Euclidean geometry in science and in practice			186
Literature			190