Episode 1
Hipparchus explains how two numbers can describe the position of a point on a sphere. He then explains stereographic projection: how can one draw a picture of the Earth on a piece of paper?
Episode 2
M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects.
Episode 3
Mathematician Ludwig Schläfli talks to us about objects in the fourth dimension and shows us a procession of regular polyhedra in dimension 4, strange objects with 24, 120 and even 600 faces!
Episode 4
Episode 5
Mathematician Adrien Douady explains complex numbers. The square root of negative numbers is explained in simple terms. Transforming the plane, deforming pictures, creating fractal images.
Episode 6
Episode 7
The mathematician Heinz Hopf describes his "fibration". Using complex numbers he builds beautiful arrangements of circles in space.
Episode 8
Episode 9
Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection.
