Unformatted text preview: 2 x1 = 0 . A.5. Prove that x 3 + x 22 x1 = 0 has no rational root, and hence that cos(2 π/ 7) is not rational. A.6. Prove that cos(2 π/ 7) is not constructible, and hence that the regular heptagon is not constructible with straightedge and compass. Note: We have now proved that the following classical problems are impossible: “doubling the cube”, “trisecting an angle”, “constructing the regular heptagon”. The only problem left is “squaring the circle”, which is equivalent to constructing π . Lindemann (1882) proved that π is not constructible, but I’m not clever enough to present the proof to you. (Wikipedia has it.)...
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This note was uploaded on 01/08/2012 for the course MATH 561 taught by Professor Armstrong during the Spring '11 term at University of Miami.
 Spring '11
 Armstrong
 Math, Algebra

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