Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses [1 ] 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
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-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.
References [ edit ]
^ 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 18, pp. 11–16, doi: 10.1007/978-3-642-24497-1_2 .
External links [ edit ]
website is http://www.dimensions-math.org/.