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?

M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects.

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!

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!

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.

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.

The mathematician Heinz Hopf describes his "fibration". Using complex numbers he builds beautiful arrangements of circles in space.

The mathematician Heinz Hopf describes his "fibration". Using complex numbers he builds beautiful arrangements of circles in space.

Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection.