### Gauss-Lucas Theorem

The Gauss-Lucas Theorem is an interesting theorem relating the roots of a polynomial P to the roots of its derivative P’.

Specifically, it states that the roots of P’ all lie within the convex hull of the roots of P.

Today I Learned

The Gauss-Lucas Theorem is an interesting theorem relating the roots of a polynomial P to the roots of its derivative P’.

Specifically, it states that the roots of P’ all lie within the convex hull of the roots of P.

This 3b1b video overviews the Borsuk-Ulam Theorem, and its applications for the Necklace Splitting problem.

It’s a super nice connection between topology and combinatorics.