  This paper is purely expository. We present short elementary proofs of
  * the Gauss Theorem on constructibility of regular polygons;
  * the existence of a cubic equation unsolvable in real radicals;
  * the existence of a quintic equation unsolvable in complex radicals (Galois
Theorem).
  The statements of these celebrated results are simple and well-known.
However, their proofs given in most textbooks rely upon much unmotivated
material and are far from being economic. We do not use the terms `Galois
group' or even `group'. The paper is accessible for students familiar with
polynomials and complex numbers, and could be an interesting easy reading for
professional mathematicians. Short English version is followed by an extended
Russian version where before presenting the proofs we illustrate the main ideas
by sequences of problems with hints or solutions.
