# Classical Impossible Constructions of Geometry proofs with Abstract Algebra.

• 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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Did you read Wikipedia? –  lhf May 2 '12 at 11:54
@lhf yes, but I have, but I have having trouble how to "say it" with abstract algebra. –  yiyi May 2 '12 at 11:58
@MaoYiyi: Do you know any Galois theory? If not, that's where to start. –  Zhen Lin May 2 '12 at 12:03
@ZhenLin, no need for Galois theory, just field theory. Except perhaps for proving that you cannot square the circle, i.e., that $\pi$ is transcendental. Hadlock solves the other two problems right at the start of the book. –  lhf May 2 '12 at 12:06
@ZhenLin no idea about that, just started learning abstract algebra. –  yiyi May 2 '12 at 12:08