подобие

In the two lectures read at school for senior pupils «Nonlinear days in Saratov for youth» the basic definitions of the theory of dimension and similarity are stated, and also some special ways for concrete problems decision, in particular, use Pi-theorem and additions of Huntley are presented. The solutions of problems from different areas of physics are shown.

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 first 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 = Axα1...xαn1 (self-similarity) appearing in various fields of science and culture. G.I. Barenblatt indicates that scaling laws never appear by accident.