2000 years unsolved: Why is doubling cubes and squaring circles impossible?

Today’s video is about the resolution of four problems that remained open for over 2000 years from when they were first puzzled over in ancient Greece: Is it possible, just using an ideal mathematical ruler and an ideal mathematical compass, to double cubes, trisect angles, construct regular heptagons, or to square circles? 00:00 Intro 05:19 Level 1: Euclid 08:57 Level 2: Descartes 16:44 Level 3: Wantzel 24:00 Level 4: More Wantzel 31:30 Level 5: Gauss 35:18 Level 6: Lindemann 40:22 Level 7: Galois Towards the end of a pure maths degree students often have to survive a “boss“ course on Galois theory and somewhere in this course they are presented with proofs that it is actually not possible to accomplish any of those four troublesome tasks. These proofs are easy consequences of the very general tools that are developed in Galois theory. However, taken in isolation, it is actually possible to present proofs that don’t require much apart from a certain familiarity with simple proofs by contradiction of the ty