11 May - 17 May

We completed the study of cyclotomic extensions. We proved that cyclotomic polynomials over the rationals are irreducible. 

We proved the Theorem of Natural Irrationalities and used it to show that the compositum of the cyclotomic fields $\mathbb{Q}(\omega_n)\cdot \mathbb{Q}(\omega_m) = \mathbb{Q}(\omega_{nm})$, where $\omega_n, \omega_m, \omega_{nm}$ are primitive $n$-th, $m$-th and $nm$-th roots of unity respectively, and $\mathrm{gcd}(n,m) = 1$.

We studied the constructibility by ruler and compass of regular polygons.