Dimensions: a walk through Mathematics (2010)

Chapter 9 : Proof

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

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

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)