
♦♦ Des racines emboîtées


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The standard identities studied in middle school (and now at the start of high school…) can prove very useful in finding the solutions to certain equations, including quadratics. The trick is knowing where these mysterious identities are hiding!

Starting with two distinct points in the plane and performing only finitely many ruler-and-compass constructions, can we obtain any point in the plane? If not, which points can we obtain in this way?

In mathematical and logical puzzles, often inspired by observations of everyday life, polynomials can crop up in surprising ways. Geometry, binary logic and algorithms, peg games, combinatorics… no field is immune!

In practice, finding an optimal value often involves computing demanding integrals. How can this be done? Physicists developed the Monte Carlo method, whose complexity does not increase with the dimension of the integrals involved.