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.
M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like.
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.
Mathematician Adrien Douady explains complex numbers. The square root of negative numbers made easy!
Transforming the plane, deforming images, creating fractal images.
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.
Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem concerning the stereographic projection.
