Question

Three geometrical problems that date back to the early days of Greek
geometry and often referred to as the Three Classical Problems, are
solved by purely geometric means using only a straight edge and a
compass. Name the three classical problems and illustrate them with
drawings.

Answer 1

There are following three problems

1. construct a square with an area exactly equal to the given circle.
2. construct an angle exactly one third of any given angle
3. construct a cube with exactly twice the volume of given cube.

This can be shown by the following figure

It was proved that these three problems are impossible to be solved with a help of previous theory or concept by purely geometry using straight edge and compass.