A regular n-gon is constructible if and only if cos(2π/n) is constructible. (a) Prove that a regular hexagon is constructible. (b) Prove that a regular 7-gon is not constructible because cos(2π/7) is a root of the irreducible polynomial 8x³ + 4x² - 4x - 1.

A regular n-gon is constructible if and only if cos(2π/n) is constructible. (a) Prove that a regular hexagon is constructible. (b) Prove that a regular 7-gon is not constructible because cos(2π/7) is a root of the irreducible polynomial 8x³ + 4x² - 4x - 1.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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