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.
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