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Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations - Softcover
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1. Algebraic Preliminaries.- 2. Algebraic Numbers and Their Polynomials.- 3. Extending Fields.- 4. Irreducible Polynomials.- 5. Straightedge and Compass Constructions.- 6. Proofs of the Geometric Impossibilities.- 7. Zeros of Polynomials of Degrees 2, 3, and 4.- 8. Quintic Equations 1: Symmetric Polynomials.- 9. Quintic Equations II: The Abel-Ruffini Theorem.- 10. Transcendence of e and π.- 11. An Algebraic Postscript.- 12. Other Impossibilities: Regular Polygons and Integration in Finite Terms.- References.- Index.
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Abstract Algebra and Famous Impossibilities : Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations
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Springer Nature B.V. Nov 2022, 2022
ISBN 10: 303105699X
ISBN 13: 9783031056994
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