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Seminar ATSS on 11 November, 2005 Error processing SSI file
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Russian Version

The Report about the Alliance meeting on the November 11, 2004

1. Lecture of Dr. Alexey Stakhov “Harmony Mathematics and its Applications in Modern Science”

Doctor of Engineering Sciences Alexey Stakhov is one of the leading specialists in the field of the modern theory of the Golden Section. He has been President of the International Club of the Golden Section since 2003 and a member of our Alliance since November 2004.

Dr. Stakhov lecture was devoted to the statement of the new mathematical direction called the “Harmony Mathematics”. The development of computer science became the reason of interest to new methods of number representation and new computer arithmetic’s, a process of the "global mathematization of sciences" became the reason of interest to the measurement problem, and cosmological researches revivaled the interest to the "Pythagorean" doctrine about numerical Harmony of the Universe. Those are the major tendencies of modern science and mathematics development. They as though return the modern science and mathematics to their beginnings on the new stage of scientific development. Here there is the idea of revision and development of mathematical achievements and fundamental concepts of antique mathematics. In it the historical preconditions for creation of new kind of "Elementary Mathematics" called the “Harmony Mathematics” consist.

In 1996 Dr. Stakhov delivered the lecture “The Golden Section and Modern Harmony Mathematics” at the 7th International Conference “Fibonacci Numbers and Their Applications” (Austria, Graz, 1996). This lecture was repeated by Dr. Stakhov at the meeting of the Ukrainian Mathematical Society (Kiev, 1998) and then at the seminar “Geometry and Physics” of the Theoretical Physics Department of the Moscow University (Moscow, 2003).

The new scientific principle, the Generalized Principle of the Golden Section underlies “Harmony Mathematics. This one includes in itself as special cases the "Dichotomy Principle" and the classical "Golden Section Principle" that came to us from the ancient science. The Generalized Principle of the Golden Section underlies the following mathematical theories, which form in total the "Harmony Mathematics": algorithmic measurement theory, a theory of number systems with irrational radices, a theory of the hyperbolic Fibonacci and Lucas functions, a theory of the Fibonacci and “Golden” matrices.

The Harmony Mathematics is the basis for the following “Golden” Projects: creation of new coding theory, new computer theory, new measurement systems theory, the reform of mathematical education, and finally, the Museum of Harmony and Golden Section as a unique collection of all Nature, Science and Art works based on the Golden Section (

2. Discussion of Dr. Stakhov’s lecture

The lecture has been listened to with great attention. Many questions concerning to new proportional coefficients of the Golden Sections that were deduced by Dr. Stakhov and also to the conclusions about the presence of infinite quantity of such coefficients have been given to the lecturer.

The “Museum of Harmony and the Golden Section” has caused great interest from the Alliance members. Many questions have been asked and many interesting propositions have been formulated stated. In particular, a special interest of the Alliance members has caused the applications of the Generalized Golden Section in Graphic Art, Architecture, Music and Poetry.

Interesting propositions have been discussed, for example, participation of Dr. Stakhov in the new Alliance projects, the edition of the Internet-Journal "Noosphere", holding the scientific seminars and conferences on the basis of the scientific direction of Dr. Stakhov.

The following Alliance members Edward Levin, Moisey Korol, Fatim Nabiulin, Ernest Zaltsberg, Rimma Vedom, Vitali Gitberg have participated in the discussion.

3. Concerning point 2 "The Report of the Alliance Board"

The President of the Alliance Vitali Gitberg informed that the Report was sent by å-mail to all Alliance members. He has told about the new events, which have been not included in the Report.

Because the time, which had been given at the Alliance meeting, almost completely was devoted to Dr. Stakhov’s lecture, the discussion of the Alliance Report practically could not take place. In this connection the President of the Alliance offered to the Alliance members to state their propositions about the Alliance Report by å-mail.

4. Miscellaneous

The President of the Alliance Vitali Gitberg presented the new Alliance members. He informed also about their opportunities to participate in the Alliance Programs and Projects.

5. Attachment to the Report

If somebody wishes to get more information about the “Harmony Mathematics” it is recommend to visit the site "Museum of Harmony and Golden Section" ( and the “Report about Dr. Stakhov’s lecture at the seminar "Geometry and Physics” of the Theoretical Physics Department of the Moscow University” (

Dr. Alexey Stakhov speaks Russian, Ukrainian and English fluently and he is prepared to give the lectures on the Harmony Mathematics at the Ontario secondary and high schools, universities and colleges. Besides Dr. Stakhov can offer his electronic books in Russian: "A New Kind of Elementary Mathematics and Computer Science, based on the Golden Section", "Hyperbolic Fibonacci and Lucas Functions: New Mathematics for the Living Nature”, "Under the Golden Section Sign: a Story of the Sun of Studbut Soldier”. You can send an email to dr stakhov for further information.

Reviews of the well-known scientists to Dr. Stakhov’s scientific direction

Doctor of Sciences in Physics and Mathematics, Professor Gennady Shypov (Moscow):

Dr. Stakhov’s lecture is irreproachable both under the form, and under the contents, that is, satisfies completely to the “Golden Section Principle”. The most impression is the fact that such serious mathematical research is executed by one person. Results of Dr. Stakhov’s researches have fundamental importance for development of mathematics and a computer science. Dr. Stakhov work is executed at so high level, that quite deserves its promotion on the Nobel Prize.

Dr. Alan Rogerson, the scientific supervisor of the International Project “Mathematical Education of the 21-th century”:

Dear Alexey,
I was fascinated to read your paper, which is full of interesting information, some of it new to me. Your ideas are far reaching and their implementation in schools is obviously the next step. Are there teachers in the Ukraine or elsewhere who have started to use your ideas and your programme? I would be most interested to hear about their experiences. Best wishes

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