Dimensions: A Walk Through Mathematics

Synopsis

In broad terms, the level of mathematics in the 9 chapters increases gradually, with the early ones being suitable for the general public and ages 12-15, and the later ones for university science students.

Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. 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; 2) Dimension three - M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like; 3 &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; 5 & 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; 7 & 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; 9) Proof - Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem concerning the stereographic projection.

Language

English

Country

France

Year of release

2010

Year of production

2010

Notes

Distributed under a Creative Commons license

Documentation

20 page booklet included with DVD

Uses

For detailed information on use see http://www.dimensions-math.org/Dim_tour_E.htm

Subjects

Mathematics

Keywords

complex numbers; geometric dimensioning and tolerancing; geometry; fourth dimension; Hopf fibration

Online availability

URI

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

Price

free

Delivery

Streamed/Download

Credits

Director

Aurélien Alvarez

Contributor

Adrien Douardy; Bernhard Riemann; Étienne Ghys; Heinz Hopf; Jos Leys; Ludwig Schläfli; M.C. Escher

Distribution Formats

Type

DVD

Format

Region 2 PAL

Price

10 euros

Availability

Sale

Duration/Size

117 minutes

Year

2011

Production Company

Name

Association des mathématiciens de l’ENS Lyon.

Email

etienne.ghysATumpa.ens-lyon.fr

Web

http://www.dimensions-math.org/Dim_E.htm External site opens in new window

Phone

+33 4 72 72 84 24

Fax

+33 4 72 72 84 80

Address

Unité de Mathématiques Pures et Appliquées
l’École Normale Supérieure de Lyon
46 Allée d’Italie
69364 Lyon
France