What would need to be possible to make a cube of circles?

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SUMMARY

A cube of circles is conceptually possible within the realm of topology, where a sphere, viewed as an infinite collection of circles, can be equivalent to a cube. Traditional geometry, which focuses on measuring angles and lengths, does not allow for the transformation of a two-dimensional shape into a three-dimensional object without losing its properties. The discussion also references the 3D Fourier transform of a square wave as a related concept, highlighting the intersection of geometry and mathematical transformations.

PREREQUISITES
  • Understanding of topology and its principles
  • Familiarity with geometric concepts, particularly dimensions
  • Knowledge of Fourier transforms and their applications
  • Basic principles of cubism in art and geometry
NEXT STEPS
  • Explore the principles of topology and its implications in geometry
  • Study the properties of 3D Fourier transforms and their applications
  • Investigate the concept of circular cubism and its artistic interpretations
  • Learn about the relationship between two-dimensional and three-dimensional shapes
USEFUL FOR

Mathematicians, artists exploring geometric concepts, and students of topology and geometry will benefit from this discussion.

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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}##)

d9GcReQEauioNj31F70jKoM3As9mate3FM5YC6z5prJFuzSQ&s.jpg
 
SheldonCooper13 said:
in what geometry would a cube of circles be possible
The 3D Fourier transform of a square wave.
 

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