Chapter 2: Dimension three discusses how two-dimensional beings would imagine three-dimensional objects.
Chapters 3 and 4: The fourth dimension talks about
four-dimensionalpolytopes (polychora), projecting the regular ones stereographically on the three-dimensional space.
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]
References
^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.
Chapter 2: Dimension three discusses how two-dimensional beings would imagine three-dimensional objects.
Chapters 3 and 4: The fourth dimension talks about
four-dimensionalpolytopes (polychora), projecting the regular ones stereographically on the three-dimensional space.
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]
References
^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.