Abstract
Living in a three-dimensional world, it is quite difficult for us to imagine a fourth geometric dimension, perpendicular to the three we already know. But a 4D geometry does not break any mathematical rule and indeed mathematicians have been studying it since the eighteenth century. Ideas referring to a 4D world have then spread beyond the math world and have inspired painters, sculptors, writers, and architects. Modern computer graphics allows us to get some more insight into this fascinating world.
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Notes
- 1.
Hypercube, Wikipedia, The Free Encyclopedia, <http://en.wikipedia.org/wiki/Hypercube> Hypercube, from MathWorld, Eric W. Weisstein, <http://mathworld.wolfram.com/Hypercube.html>
- 2.
The word hypersphere can in general describe any higher-dimensional analog of the sphere (i.e., spheres in four, five, six, etc. dimensions).
- 3.
3-sphere, Wikipedia, The Free Encyclopedia. <http://en.wikipedia.org/w/index.php?title=3-sphere%26oldid=208966785> Hypersphere, from Math World, Eric W. Weisstein, <http://mathworld.wolfram.com/Hypersphere.html>
- 4.
120-cell, Wikipedia, The Free Encyclopedia, <http://en.wikipedia.org/wiki/120-cell>120-cell, from MathWorld, Eric W. Weisstein, <http://mathworld.wolfram.com/120-Cell.html>
- 5.
Bonds of Friendship, J. Robinson, <http://www.bradshawfoundation.com/jr/bonds_of_friendship.php>
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Todesco, G.M. (2010). Four-Dimensional Ideas. In: Capecchi, V., Buscema, M., Contucci, P., D'Amore, B. (eds) Applications of Mathematics in Models, Artificial Neural Networks and Arts. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8581-8_26
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