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.
SheldonCooper13
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in what geometry would a cube of circles be possible
 
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Circular cubism?
 
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SheldonCooper13 said:
in what geometry would a cube of circles be possible
None that I can think of. A cube is a three-dimensional object, while circles are two-dimensional.
 
SheldonCooper13 said:
in what geometry would a cube of circles be possible
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.

Not that we haven't tried: (##\sim 3,000 - 2,000 \text{ BC}##)

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SheldonCooper13 said:
in what geometry would a cube of circles be possible
The 3D Fourier transform of a square wave.
 

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