High School 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.
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in what geometry would a cube of circles be possible
 
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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