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  • Trisecting an angle (dividing a given angle into three equal angles),
  • Squaring a circle (constructing a square with the same area as a given circle), and
  • Doubling a cube (constructing a cube with twice the volume of a given cube).

Told that these problems could only be proved with abstract algebra. I have no idea how to start. I have found this page.

I have an idea of what is being said, but no idea about how to exactly prove this. Any pointers would be helpful.

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    @MaoYiyi, see my answer.2012-05-02

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Field theory and its classical problems by Hadlock is a wonderful book motivated by these problems.

See also Geometry: Euclid and Beyond by Hartshorne.

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    @DaveL.Renfro, thanks for the reference to Bold's book. I didn't know that book.2012-05-03