- #1
SheldonCooper13
- 5
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in what geometry would a cube of circles be possible
B What would need to be possible to make a cube of circles?
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A cube of circles is conceptually challenging due to the dimensional differences between three-dimensional cubes and two-dimensional circles. In topology, a sphere can represent an infinite collection of circles, suggesting a theoretical equivalence to a cube. However, traditional geometry, which involves measuring angles and lengths, cannot reconcile the roundness of circles with the edginess of cubes. Historical attempts to explore this concept date back to around 3000-2000 BC. The discussion also mentions the 3D Fourier transform of a square wave as a potential mathematical exploration of this idea.
- #2
- 29,271
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Circular cubism?
- #3
Mark44
Mentor
- 38,046
- 10,541
None that I can think of. A cube is a three-dimensional object, while circles are two-dimensional.SheldonCooper13 said:
- #4
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It is possible in topology where a sphere that can be considered as an infinite collection of circles is equivalent to a cube. Geometry means that we can measure angles and lengths. This makes it impossible to get something edgy out of something round.SheldonCooper13 said:
Not that we haven't tried: (##\sim 3,000 - 2,000 \text{ BC}##)
- #5
Baluncore
Science Advisor
- 16,558
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The 3D Fourier transform of a square wave.SheldonCooper13 said: