Let $\mathcal{C}_d\subset \mathbb{C}^{d+1}$ be the space of non-singular, univariate polynomials degree $d$. The Vi\`{e}te map $\mathscr{V} : \mathcal{C}_d \rightarrow Sym_d(\mathbb{C})$ sends a polynomial to its unordered set roots. It is classical fact that induced $\mathscr{V}_*$ at level fundamental groups realises an isomorphism between $\pi_1(\mathcal{C}_d)$ and Artin braid group $B_d$. F...