ISSN 0869-6632 (Online)
ISSN 2542-1905 (Print)

Cite this article as:

Trubeckov D. I. Two lectures about the two ways of symmetry investigation. Izvestiya VUZ, 2013, vol. 21, iss. 4, pp. 13-33. DOI:


Two lectures about the two ways of symmetry investigation

Trubeckov Dmitrij Ivanovich, Saratov State University

These lectures were delivered to the high school students at the School – seminar «Nonlinear Days for Youth in Saratov – 2012» in October 2012. They present the two ways of historical investigation of symmetry. The ?rst way is self-similarity, i.e. invariance at dimension scale changing. In a more general way the term «scaling» is used, meaning the existence of power-law correlation between some variable and variables x1, ...xn: y = Ax?1...x?n1 (self-similarity) appearing in various ?elds of science and culture. G.I. Barenblatt indicates that scaling laws never appear by accident. They always reveal the most important property of the phenomenon under consideration: its self-similarity. The term self-similarity means that changing in time and space, a phenomenon repeats itself in changed temporary and / or space scales. Lecture 2 describes the second way of symmetry investigation. It is search for solutions of algebraic equations which led to creation of group theory. As a background the lecture includes historical events and characters dealing with the described scienti?c investigations.

Key words: 

1. Стюарт Иэн. Истина и красота. Всемирная история симметрии. М.: Изд-во Астрель: CORPUS, 2010. 461 с. 2. Кессельман В. Занимательная математика. М.: АСТ-Астрель, 2008. 224 с. 3. Гутер Р., Полунов Ю. Джироламо Кардано. Гений времени и места. М.: ЭНАС,  2010. 256 с. 4. Тихомиров В. Абель и его великая теорема // Квант. 2003, No 1. С. 11. 5. Оре О. Замечательный математик Нильс Хенрик Абель. М.: Гос. изд-во физико-математической литературы, 1961. 343 с. 6. Инфельт Л. Эварист Галуа. Избранник Богов. М.: Изд-во ЦК ВЛКСМ «Молодая гвардия», 1958. 367 с.

Short text (in English):