Slavonic "Golden" Group

The outstanding Hungarian geometer Janos Boljai, one of the creators of the non-Euclidean geometry once wrote the following remarkable words:

"For the ideas, as well as for the plants, the time came when they mature in the miscellaneous places, just as in the spring the violets occur everywhere where the Sun shines".

The histories of science still should be answered a question, why just the 80th and 90th years of the 20-th century became by that historical period, when the interest in Fibonacci numbers and golden section shoved in the specially concentrated form. Just in this period the scientists of the different scientific directions have put forward the hypotheses connected to the usage of the golden proportion and made discoveries, which have fundamental significance for development both the science as the whole and its separate branches.

First of all it is necessary to mention about the original Fibonacci direction arisen in the 70th years in the Soviet science. As is known, the Fibonacci mathematicians consider Fibonacci's problem of "rabbits reproduction" as the source of their investigations. But the problem of "rabbits reproduction" is not the only problem suggested by Fibonacci. It is well known Fibonacci's problem of "choosing the best system of the standard weights" called also the "weighing problem" or "Bashet-Mendeleev's problem in the Russian historic-mathematical literature. The Ukrainian scientist Alexey Stakhov in the book "Introduction into Algorithmic Measurement Theory" (1977) and then in the brochure "Algorithmic Measurement Theory" (1979) generalized the "weighing problem" and created the new measurement theory, the algorithmic measurement theory.

Stakhov's book 'Introduction into the Algorithmic Measurement Theory' (1977)Stakhov's brochure 'Algorithmic Measurement Theory' (1979)

Just these two works issued in the end of the 70th determined the applied nature of the researches in the Fibonacci field (Fibonacci codes, Fibonacci arithmetic, Fibonacci computers), which then begun to develop in the Soviet science. Just this scientific direction is a distinctive peculiarity of the Soviet scientific school in the Fibonacci field in comparison with the American Fibonacci Association.

The year of 1984 was the most successful for the golden section. In November 12, 1984 in the small article published in the authoritative Journal "Physical Review Letters" it was given the experimental evidence of the existence of the metal alloy with exclusive properties (the Israel physicist Dan Shechtman was the author of this discovery. The crystalline structure of this alloy had "icosahegral" symmetry, that is, the symmetry of the 5-th order that is strictly forbidden by the classic crystallography. The alloys with such exotic properties were called as quasi-crystals. Due to this discovery the golden section, which underlies the basis of the regular icosahedron and symmetry of the 5-th order (the pentagram) moved forward to the first roles in the modern physics. In Gratia's article "Quasi-crystals" (1988), dedicated to this discovery it is noted that "its significance in the mineral world can be put in one row with the addition of the irrational numbers concept in mathematics".

In 1984 two books dedicated to the golden section were published. The Byelorussian philosopher Eduard Soroko in the book "Structural harmony of systems" makes the courageous attempt to revive in modern science the Pythagorean idea about numeric harmony of the Universe and states so-called the "Law of structural harmony of systems" expressed with the help of the concept of the generalized golden sections, the golden ­-sections, which are the generalization of the classic golden section.

Eduard Soroko's book 'Structural harmony of systems' (1984)Stakhov's book 'Codes of Golden Proportion' (1984)

In the same year Stakhov's book "Codes of the Golden Proportion" was published; in this book the number systems with irrational bases called the "codes of the golden proportion" and being the development of Bergman's number system were developed.

Note that in 1984 the Fibonacci Association actuates considerably its activity; just in this year the First International Conference on Fibonacci Numbers and Their Applications was hold. Starting since this year the holding of this famous mathematical Fibonacci conference becomes regular (once for 2 years).

One year later (1985) the book "Aesthetic foundations of the Ancient Egypt Art" by the Russian art critic Natalie Pomerantseva was published; in the book it was shown enough convincingly the role of the golden section in the Ancient Egypt culture.

Natalie Pomerantseva's book 'Aesthetic foundations of the Ancient Egypt Art' (1985)

The year of 1986 was marked by the publication of two books on the golden section. In Poland the book of the Polish scientist and journalist Jan Grzedzielski "Energy-Geometric Code of the Nature" was published in 1986. In this book, probably, for the first time the attempt was made to uncover the physical sense of the golden proportion as the main code of the Nature, as the proportion of the thermodynamic equilibrium of the self-organizing systems. In the same year the teacher of the Kiev State Art Institute Kovalev published the manual for the artists "The Golden Section in Painting".

Jan Grzedzielski's book 'Energy-Geometric Code of the Nature' (1986)Kovalev's book 'The Golden Section in Painting' (1986)

The beginning of the 90th was marked by the publication of two books on the golden section. The former of them is the book "The Golden Section: three Views on the Nature of Harmony" (1990). Three authors, the representatives of the Art, the Russian architect Shevelev, the Russian composer Maruitaev, and the Russian architect Shmelev wrote this one. As is asserted in the abstract, "the book is dedicated to the theoretical substantiation of the golden section phenomenon, one of the universal regularities of harmony".

Shevelev, Maruitaev, Shmelev 'The Golden Section: three Views on the Nature of Harmony' (1990)Vasutinski's book 'The Golden Proportion' (1990)

The popular book "The Golden Proportion" written by the Ukrainian scientist, chemist, geologist, metallurgist and mechanic Vasutinski was the considerable event of the year of 1990. In the book written with the great skill "the manifestation of the golden proportion regularities in the architecture, music, poetry, and also in chemistry, biology, botanic, geology, astronomy, engineering is described".

In the beginning of the 90th there became clear that in the Slavonic science (Ukraine, Russia, Byelorussia, Poland) the powerful group of scientists, the representatives of different sciences and arts, the authors of the rather original publications in the golden section field was formed. There was the idea to join together all these scientists and to create some "golden" scientific society. According to the initiative of the Ukrainian scientist Prof. Alexey Stakhov the First International Seminar "The Golden Proportion and Problems of System Harmony" was hold .in Kiev in 1992. The Byelorussian philosopher Doctor of Philosophical Sciences Eduard Soroko (Minsk), the Ukrainian architect, Doctor of Art Criticism ╬leg Bodnar (Lvov), the Ukrainian mathematician and economist, Doctor of Economical Sciences Ivan Tkachenko, The Russian mechanic, Doctor of Engineering Sciences Victor Korobko (Stavropol), the Ukrainian anatomist, Doctor of Medical Sciences Pavel Shaparenko (Vinnitsa), the Ukrainian chemist, PhD in Chemical Sciences Nikolay Vasutinski (Zaporozhye), the Polish journalist Jan Grzedzielski were the members of the Organizing Committee. This group of the scientists became the skeleton of the Slavonic scientists association called as the "Slavonic "Golden" Group".

The Second International Seminar "The Golden Proportion and Problems of System Harmony" was hold in 1993 in Kiev and then according to Prof. Korobko's initiative the Seminar continued its work in Stavropol (Russia) in 1994, 1995 and 1996.

The seminar rendered a great influence on activating the researches in the golden section field and the members of the Slavonic "Golden" Group in the 90th published a number of the interesting books in this field.

In 1994 the book by Prof. Bodnar "The Golden Section and non-Euclidean geometry in the Nature and Art" was published.

Bodnar's book 'The Golden Section and non-Euclidean geometry in the Nature and Art' (1994)

The new geometrical theory of phyllotaxis (the "Law of the spiral bio-symmetry transformation") developed by Bodnar is the main outcome of the book.

In 1996 there was issued the book by Prof. Subbota (St.-Petersburg) "The Golden Section ("Sectio Aurea") in medicine". In the book "it was shown the universality of the golden section manifestation in the constitution of the man's organs and systems, and also in their functional parameters. The values of deviations from the golden section are established at the effect on the organism of the unfavorable environmental factors and at some diseases".

However the year of 1997 became the most fruitful for the Slavonic "Golden" Group. In this year the literature on the golden section was added with three books written by the Slavonic scientists.

The book "The Gold Proportion and Problems of System Harmony" by Prof. Korobko (Russia), the active member of the "Slavonic "Golden" Group", was published in 1997. The book is written under direct influence of the International Seminar "The Golden Section and Problems of System Harmony" (1992-1995).

Korobko's book 'The Gold Proportion and Problems of System Harmony' (1997)

The book contains a vast material testifying about manifestation of the golden section in the miscellaneous areas of the Nature, Science and Art. The feature of the book is the fact that it can serve as educational and scientific-methodical manual for the teachers, post-graduate students both the engineering and humanitarian colleges and universities for the academic disciplines "Foundations of System Harmony", "Philosophy", "Ethics and Aesthetics" and so on. The Russia Association of the Building Universities recommends the book as the manual for the students of colleges and universities.

In 1997 the Russian biologist Prof. Zvetkov published the book "Heart, Golden Section and Symmetry".

Zvetkov's book 'Heart, Golden Section and Symmetry' (1997)

The book is the total of the author's long-lived researches in the field of the golden section applications to the mammals cardiac activity. In the book "the set of golden sections in the different structures of the cardiac cycle is established". The role of the golden section and Fibonacci numbers in the optimization of the heart activity (the minimization of energy consumption, blood, muscle and vascular matter) is shown.

At last, the book of the Ukrainian scientist Alexey Stakhov titled "Computer Arithmetic based on Fibonacci numbers and golden section: new information and arithmetic computer foundations" is one more book in the field of the golden section issued to the public in 1997. The book is the further development of the previous author's books "Introduction into Algorithmic Measurement Theory" (1977) and "Codes of the Golden Proportion" (1984) pointed out on the development of the "non-traditional arithemetics" for computers of the future generation. The "Ternary Mirror-Symmetrical Arithmetic" is the new result of the book. From the last publications of the same author it is necessary to mark the book "Introduction into Fibonacci coding and cryptography", published by Stakhov in the co-authorship with Vinancio Massingue (Mozambique) and Anna Sluchenkova (Canada) in 1999.

Stakhov's book 'Computer arithmetic based on Fibonacci numbers and golden section: new information and arithmetic computer foundations' (1997)Alexey Stakhov, Vinancio Massingue (Mozambique) and Anna Sluchenkova (Canada) 'Introduction into Fibonacci coding and cryptography' (1999)

What conclusions can be made from this review of the modern publications on the Fibonacci numbers, the golden section and their applications? Still Poincare wrote, that many ways lead to the city with a mysterious title "The Secrets of the Universe"; it is possible to enter to it both through the gate of music and through the gate of mathematics and through any other branches of knowledge, - if only to penetrate in them rather deeply. However it is clear that some gates can appear closer and other further from the center of this conditional city of the "global problems". However there are the gates where the ways of many sciences converge. One of them is the gate with the surprising title of "The Golden Section". Through it, probably, the most short way up to the center lies, in which there is the main "Secret of the Universe, the "Laws of the Universe Harmony".

The splash of the interest in the golden section, problems of harmony and symmetry reflects an objective path of development of modern science, which is moving to uncovering the laws of the Universe harmony, creation of the new scientific picture of the World on their basis and renewal of the deep connections between Science and Art, the two mutually complementing one another methods of the objective Universe harmony reflection.

In modern science there are two scientific teams professionally learning the Fibonacci numbers, the golden section and their applications. The Fibonacci Association is the undoubted leader in mathematical Fibonacci researches. However the "Slavonic "Golden" Group" has the undoubted successes in the applications of the Fibonacci numbers and the golden section. The coordination of the efforts of these two professional scientific collectives can promote to the solution of one of the major problems of modern science, the creation of the "Science of System Harmony" where the Fibonacci numbers and the golden section could take a worthy place.