Dimensions (animation)

For other uses, see Dimension (disambiguation).

Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry.[1] It uses POV-Ray to render some of the animations, and the films are released 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 talks about four-dimensional polytopes (polychora), projecting the regular ones stereographically on the three-dimensional 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.

They are available for download in several languages.[2]

  1. ^ Alvarez, Aurélien; Leys, Jos (2012), "Dimensions, a Math Movie", Mathematics and Modern Art: Proceedings of the First ESMA Conference, held in Paris, July 19-22, 2010, Springer Proceedings in Mathematics, vol. 18, pp. 11–16, doi:10.1007/978-3-642-24497-1_2.
  2. ^ "Clay Award for Dissemination | Clay Mathematics Institute". Archived from the original on 2020-02-27. Retrieved 2016-03-02.