Dimensions

Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence.

The fourth chapter, showing the stereographic projection of a polychoron on our three-dimensional space.

The film is separated in nine chapters, which follow this plot:

Chapter 1: Dimension two explains Earth's coordinate system, and introduces the stereographic projection.
Chapter 2: Dimension three discusses how two-dimensional beings would imagine three-dimensional objects.
Chapters 3 and 4: The fourth dimension talk about four-dimensional polytopes (polychora), projecting the regular ones stereographically on the three-dimentional space.
Chapters 5 and 6: Complex numbers are about the square root of negative numbers, transformations, and fractals.
Chapters 7 and 8: Fibration show what a fibration is. Complex numbers are used again, and there are circles and tori rotating and being transformed.
Chapter 9: Proof emphasizes the importance of proofs in mathematics, and proves the circle-conservationess of the stereographic projection as an example.