“Nothing is impossible!" While it is comforting to believe this greeting card sentiment — it's the American dream, after all — there are impossible things. Ancient Greek geometers and future generations of mathematicians tried and failed to square circles, trisect angles, double cubes, and construct regular polygons using only a compass and straightedge. Join David Richeson, Professor of Mathematics at Dickinson College and Editor of Math Horizons, to try your hand at some of these unusual geometric construction techniques. But get ready to fail — after two thousand years, all four of these “problems of antiquity” have been proved to be mathematically impossible!