Squaring the Circle, or Entertaining Geometry

What is squaring the circle, and why have not only mathematicians but also presumptuous seekers of fame sought to solve this problem? It is stated as follows: "How to construct a square whose area is equal to the area of... a given circle?" The problem does not seem so difficult, but the search for its solution is compared to concocting the elixir of life, searching for the philosopher's stone, as well as inventing a perpetual motion machine.
Yakob Isidorovich Perelman invites you to participate in solving this ancient puzzle. Learn more about squaring the circle and solve the problems prepared by the great mathematician and popularizer of science.