Why Is Doubling Cubes and Squaring Circles Impossible?

Explore a 40-minute video that delves into the resolution of four ancient Greek mathematical problems that remained unsolved for over 2000 years. Learn why doubling cubes, trisecting angles, constructing regular heptagons, and squaring circles are impossible using only an ideal mathematical ruler and compass. Follow the progression of mathematical understanding through seven levels, from Euclid to Galois, as the video explains the proofs behind these impossibilities. Gain insights into the development of mathematical thought and the tools used to solve complex geometrical problems. Discover how these seemingly simple tasks led to profound advancements in mathematics, including Galois theory. Benefit from recommended further reading and additional resources to deepen your understanding of these classical mathematical challenges.

Intro.
Level 1: Euclid.
Level 2: Descartes.
Level 3: Wantzel.
Level 4: More Wantzel.
Level 5: Gauss.
Level 6: Lindemann.
Level 7: Galois.