  # Dimensions: a walk through Mathematics (2010) Chapter 3: The fourth dimension

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### Video Description

Mathematician Ludwig Schlafli 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!

http://www.dimensions-math.org/Dim_CH3_E.htm

### Documentary Description

A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed!

Chapter 1 - Dimension two: 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?

Chapter 2 - Dimension three: M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects.

Chapters 5 and 6 - Complex Numbers: 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.

Chapters 7 and 8 - Fibration: The mathematician Heinz Hopf describes his "fibration". Using complex numbers he builds beautiful arrangements of circles in space.

Chapter 9 - Proof: Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection.

Film produced by:
Jos Leys (Graphics and animations)
Étienne Ghys (Scenario and mathematics)
Aurélien Alvarez (Realisation and post-production)