A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed!
Dimension Two - Hipparchus shows us how to describe the position of any point on Earth with two numbers... and explains the stereographic projection: how to draw a map of the world.
Dimension Three - M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like.
The Fourth Dimension - Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension... and shows a parade of four-dimensional polytopes, strange objects with 24, 120, and even 600 faces!
Complex Numbers - Mathematician Adrien Douady explains complex numbers. The square root of negative numbers made easy! Transforming the plane, deforming images, creating fractal images...
Fibration - Mathematician Heinz Hopf explains his "fibration". Using complex numbers he constructs pretty patterns of circles in space. Circles, tori... everything rotating in four-dimensional space.
Proof - Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem concerning stereographic projection.