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Geometric Constructions

Compass-and-straightedge constructions of the ancient Greeks recast through field theory, building toward which lengths and angles can and cannot be constructed.

A Complete Introduction to Abstract Algebra, Geometric Constructions

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3 exercises

Exercise 1

Let $\theta\in[0,\frac{\pi}{2}]$ . Prove that $\sin\theta$ is constructible if and only if $\cos\theta$ is constructible.

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Exercise 2

Prove 1.38.

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Exercise 3

Prove that $8x^{3}-6x-1$ is irreducible over $\mathbb{Q}$ .(Hint: transformation before checking irreducibility.)

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