- #1
SheldonCooper13
- 5
- 0
in what geometry would a cube of circles be possible
What would need to be possible to make a cube of circles?
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Discussion Overview
The discussion revolves around the concept of a "cube of circles," exploring the geometrical and topological implications of combining three-dimensional and two-dimensional shapes. Participants examine the feasibility of such a construct within various mathematical frameworks, including geometry and topology.
Discussion Character
- Exploratory, Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- One participant questions the possibility of a cube of circles, noting the dimensional disparity between three-dimensional cubes and two-dimensional circles.
- Another participant suggests the idea of "circular cubism" as a potential conceptual framework.
- A different participant proposes that in topology, a sphere, which can be viewed as an infinite collection of circles, is equivalent to a cube, indicating a possible avenue for exploration.
- One participant asserts that traditional geometry, which involves measuring angles and lengths, makes it impossible to derive a cube from something inherently round like circles.
- Another participant introduces the concept of the 3D Fourier transform of a square wave as a potential mathematical approach to the idea of a cube of circles.
Areas of Agreement / Disagreement
Participants express differing views on the feasibility and interpretation of a cube of circles, with no consensus reached on a definitive answer or framework.
Contextual Notes
Participants highlight limitations related to dimensionality and the definitions of geometry and topology, but these remain unresolved within the discussion.
- #2
- 29,525
- 21,308
Circular cubism?
- #3
Mark44
Mentor
- 38,089
- 10,638
None that I can think of. A cube is a three-dimensional object, while circles are two-dimensional.SheldonCooper13 said:
- #4
- 20,815
- 28,452
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
2025 Award
- 16,784
- 10,433
The 3D Fourier transform of a square wave.SheldonCooper13 said:
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