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source: It's so blatant 2013年9月12日

Chapter 1: 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.

Chapter 2: Dimension three

M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what

three-dimensional objects look like.

Chapters 3 and 4: 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 !

Chapters 5 and 6: Complex numbers

Mathematician Adrien Douady explains complex numbers. The square root of negative numbers made easy !

Transforming the plane, deforming images, creating fractal images...

Chapters 7 and 8: 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.

Chapter 9: Proof

Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves

a theorem concerning the stereographic projection.

Film produced by:

Jos Leys (Graphics and animations)

Étienne Ghys (Scenario and mathematics)

Aurélien Alvarez (Realisation and post-production)

For more information on the film visit: http://www.dimensions-math.org/Dim_E.htm

Dimensions | Chapter 1 14:01

Dimensions | Chapter 2 13:46

Dimensions | Chapter 3 14:08

Dimensions | Chapter 4 13:45

Dimensions | Chapter 5 13:43

Dimensions | Chapter 6 13:35

Dimensions | Chapter 7 13:45

Dimensions | Chapter 8 13:51

Dimensions | Chapter 9 13:49

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