Every Unsolved Geometry Problem That Sounds Easy

Draw any closed loop that never crosses itself, and there will always be four points on it that form a square. Every mathematician believes it. Nobody can prove it. Nine geometry problems a schoolkid can understand that are still unsolved: Toeplitz's inscribed square, billiards in an obtuse triangle, shortest road networks and the Gilbert–Pollak conjecture, the Erdős–Szekeres happy ending problem, coloring the plane and the Hadwiger–Nelson problem, Reinhardt's worst shape for packing, Lebesgue's universal cover, Dürer's unfolding problem, and the kissing number in five dimensions. 00:00 A square in a loop 01:53 Triangle billiards 03:44 Roads between towns 05:38 The happy ending 07:29 Coloring the plane 09:10 The worst shape to pack 10:56 The universal cover 12:47 Dürer's unfolding 14:30 How many balls touch one #math #geometry #unsolvedproblems