Definitions for dimensions
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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 released under a Creative Commons licence. 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, 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.
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