of the International Conference
"Problems of Harmony, Symmetry and the Golden Section in Nature, Science and Art"
Vinnitsa State Agricultural University
Vinnitsa, Ukraine
October 22-25, 2003

Since Plato's point of view and generally since point of view of all antique cosmology, the Universe represents by itself certain proportional whole, subordinating to the law of harmonic division - Golden Section The ancient Greeks system of space proportions is presented sometimes in literature as a funny outcome of unrestrained and wild fantasy. In such explanations we can see antiscientific feebleness of those who it declares. However we can understand the given historical-aesthetic phenomenon only in connection with complete understanding of history, using dialectical-materialistic idea about culture and searching the answer in features of the antique public life.
Alexey Losev, the Russian 20th Century Thinker and Philosopher

The present stage in development of science is characterized by great interest to the doctrine about numerical Universe harmony created by Pythagoreans, to the "Sacred Geometry", created by the antique scientists, and to the "sacred knowledge", contained in Talmud, Bible, Chinese "Book of Changes" and other ancient texts. This direction of human culture stands on the high-power scientific base created by works of the outstanding scientists and thinkers of mankind: the great Greeks Pythagoras, Plato, Euclid, the great Italians Fibonacci, Leonardo da Vince, Luca Pacioli, the genius astronomer Johannes Kepler, the French mathematicians Lucas and Binet, the German scientific Zeising, the great geometer Felix Klein.

The Golden Section and connected to it Fibonacci numbers penetrate through all history of Art. Moreover, the Golden Section became an aesthetic canon of antique culture and culture of the Renaissance Epoch. In the second half of the 20th century the interest in Fibonacci numbers and the Golden Section arises in mathematics. The famous brochure "Fibonacci Numbers" by the Soviet mathematician Nikolai Vorob'ev published for the first time in 1961 and then multiply republished and translated on many languages became the textbook joined many researchers in various areas of Science and Art to the "Golden Section" and "Fibonacci numbers". The outstanding American mathematician Verner Hoggatt was the next enthusiast who understood importance of this direction for development of modern science and mathematics. Just thanks to his initiative the mathematical Fibonacci Association was established in USA in 1963. Since the same year the Fibonacci Association begun to publish the mathematical journal "The Fibonacci Quarterly" and since 1984 to hold regularly (once per 2 years) the International Conferences "Fibonacci Numbers and their Applications"

The International Conference "Problems of Harmony, Symmetry and the Golden Section in Nature, Science and Art" was held in Vinnitsa (Ukraine) on the basis of the Vinnitsa State Agricultural University. The main purpose of the Conference was to unite the efforts of the Slavonic Fibonacci-scientists in development of this important scientific direction and to discuss new achievements in this area. More than 50 outstanding Slavonic scientists representing such world famous scientific centres as Moscow, St.-Petersburg, Kiev, Minsk, Rostov-Don, Saratov, Kostroma, Vinnitsa took part in the Conference. The Proceedings of the Conference included about 80 papers was published.

The Conference notes that the origin of such high-power information means as Internet promoted to combining contributors in this area and attracting attention to this important scientific direction. It is surprising that on the Internet it is exhibited now about 4 millions sites where Fibonacci numbers and the Golden Section are mentioned! And this number is the most convincing evidence of huge interest in Fibonacci numbers and the Golden Section in modern culture, moreover, this fact confirms active process of modern science "Fibonaccization" that is one of the major tendencies in development of modern culture. Also there are all reasons to suppose that just this process can be finished by creation of new interdisciplinary science, "Sciences of System Harmony", which could become a source of new ideas for development of philosophy, history of science, mathematics, physics, chemistry, biology, economy, computer sciences and electric communication, linguistics, poetry, music, architecture!

The Conference resolves:

  1. To note an outstanding contribution of the Slavonic science to development of problems of Harmony and Symmetry and to development of the Fibonacci numbers and the Golden Section theory and its numerous applications in science, engineering, social sphere, and art (see Appendixe 1, Appendixe 2, Appendixe 3).
  2. To note the important consolidating role of the site "Museum of Harmony and the Golden Section" ( presented in 2001 on the Internet in Russian and English languages (authors Alexey Stakhov, Ukraine and Anna Sluchenkova, Canada) and recognized in 2003 by one of the best sites of a similar type by the Russian Informational Network "The Best in the Internet".
  3. To recommend to the scientists, working in this direction, to concentrate their efforts on the solution of the following problems:
    1. Development of the "Structural Harmony of Systems", based on the generalized Golden Sections and putting as the main purpose revealing of the most general regularities in structures of self-organizing systems.
    2. Development of "Mathematics of Harmony" as a new mathematical direction affecting the basis of mathematics (new measurement theory, new number theory based on generalized Golden Sections, a new class of the "golden" algebraic equations, theory of hyperbolic Fibonacci and Lucas functions, Fibonacci matrices, etc.); their main applications are computer science and simulation of harmonic processes in the alive and mineral nature.
    3. Development of the Computer Science theory based on Fibonacci numbers and the Golden Section (the project " of Fibonacci Computer, new coding theory based on the Fibonacci matrices, new theory of analog-to-digit conversion, Fibonacci's algorithms of digital signal processing, new theory of electric communication, etc.).
    4. Creation of theoretical bases of the new physics concept with use of the Golden Section and Harmony and Symmetry concepts.
    5. Development of the new concept of mathematical education based on the concepts of Symmetry, Harmony and the Golden Section.
    6. Development of artistic works based on the generalized Golden Sections.
    7. Development of the generalized Golden Sections applications in botany, biology and medicine.
    8. Revealing quantitative regularities of development of a conceptual means of humanitarian and natural sciences (economy, sociology, psychology (semiology), linguistics, pedagogic, biology, medicine, etc.), based on the Golden Section, Symmetry and Harmony.
    9. Creation of a new science, "Sciences of System Harmony", the main interdisciplinary science of the 21th century, should become the final aim of these researches.
  4. To support the initiative of the International Symmetry Association (ISA) on creation of the International Club of the Golden Section (ICGS) in frameworks of ISA under scientific supervision of Dr. Prof. Alexey Stakhov.
  5. To recommend to all participants of the Conference and members of ICGS to prepare and submit to the Club President scientific projects on a solution of problems in various scientific areas with use of principles of the Golden Section, Symmetry and Harmony (May 2004).
  6. To recommend ICGS to include the following scientists to the Scientific Council of the Club:
    Shevelev I. (Kostroma), Soroko E. (Minsk), Petuokhov S. (Moscow), Vladimirov Ju. (Moscow), Korobko V. (Minsk), Bodnar Ja. (Lvov), Voloshinov A. (Saratov), Vishnjakov Ju. (Taganrog), Grinbaum O. (St.-Petersburg), Kudrevatova O. (Moscow), Kharitonov A. (Moscow), Marutaev M. (Moscow), Shaparenko P. (Vinnitsa), Malygin A. (Moscow), Subbota A. (St.-Petersburg), Tsvetkov V. (Puschino), Veize D. (Moscow), Tatarenko . (Rostov-Don), Maiboroda A. (Rostov-Don), Jasinski C. (St.-Petersburg), Semenjuta N. (Homel).
  7. To recommend to the International Club of the Golden Section to concentrate its efforts on realization of the following projects:
    1. Development and extension of the site "Museum of Harmony and Golden Section" (, which should become the peculiar Internet encyclopaedia of the Golden Section.
    2. Architectural realization of the Museum of Harmony and Golden section. The Conference notes an extremely important significance of this project in development of human culture for forming of new scientific outlook based on principles of Harmony, Symmetry and the Golden Section.
    3. Establishment of the Journal "The Golden Section: Theory and Applications" (in Russian and English languages).
    4. Creation of the "Fund of the Golden Section" for financial encouragement of the best works, projects on the Golden Section, Symmetry and Harmony and scientists actively working in this area.
    5. Organization of lecturer collectives including the leading members of the International Club of the Golden Section with the purpose of worldwide popularization of knowledge on Harmony, Symmetry and the Golden Section.
  8. To recommend to Ministries of Education of Russia, Ukraine, Belarus, USA, Canada, Australia and other countries to enter into the educational plans of all specialities new educational disciplines "Harmony of Systems", "Fibonacci Arithmetic, Coding and Computers", and "Mathematics of the Golden Section" (see Appendixe 4).
  9. To support the initiative of the Moscow Publishing House "Cyrillic" about issuing of the books and brochures on the Golden Section problem within the framework of the series "The Golden Section" under scientific Dr. Prof. Stakhov edition.
  10. To recommend to organizers of the Conference and President of the International Club of the Golden Section to address to known funds, UNESCO and United Nations Organization (special divisions) behind scientific and financial support of the projects and works of the members of the International Club of the Golden Section.
  11. To consider expedient regular (once per 2 years) holding the International Conferences "Problems of Harmony, Symmetry and the Golden section in Nature, Science and Art". To ask the International Club of the Golden Section to undertake the initiative on organization of such Conferences.
  12. To express thanks to the Vinnitsa State Agricultural University for excellent organization of the Conference.
  13. To send the given Resolution to Academies of Sciences and Ministries of Education of Russia, Ukraine, Belarus, USA, Canada, Italy, Greece, Australian Academy of Sciences, International Council of Scientific Unions, International Symmetry Association (Hungary), Fibonacci Association, special divisions of UNESCO and United Nations Organization.
Chairman of the Organizing Committee
Rector of the Vinnitsa State Agricultural University, Professor,
Academician of the International Academy of Higher School
Leonid Sereda
Scientific Coordinator of the Conference
Doctor of Sciences in Computer Science, Professor
Academician of the Academy of Engineering Sciences of Ukraine
President of the International Club of the Golden Section
Alexey Stakhov