Dimensions (animation)

• 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, 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.