Episoade 9
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?
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Dimension Three
M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects.
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The fourth dimension (1)
Mathematician Ludwig Schläfli 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!
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The fourth dimension (2)
Mathematician Ludwig Schläfli 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!
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Complex Numbers (1)
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.
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Complex Numbers (2)
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.
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Fibration (1)
The mathematician Heinz Hopf describes his "fibration". Using complex numbers he builds beautiful arrangements of circles in space.
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Fibration (2)
The mathematician Heinz Hopf describes his "fibration". Using complex numbers he builds beautiful arrangements of circles in space.
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Proof
Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection.
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