Answer to Question #134051 in Geometry for Kholi

Question #134051
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.
1
Expert's answer
2020-09-21T15:18:16-0400


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.


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