# Dimensions: A Walk Through Mathematics

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 the stereographic projection. Support the authors and buy the DVD here.

**Watch the full documentary now (playlist)**