The two dimensional regular polygons.

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Discussion Overview

The discussion revolves around the nature of two-dimensional regular polygons and their implications for the dimensions of length and breadth in the universe. Participants explore the mathematical and physical connections between the properties of polygons and the continuity of space, questioning the consequences of a finite series of regular polygons.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the series of two-dimensional regular polygons is infinite, while questioning the implications of a finite series on the universe.
  • One participant distinguishes between the mathematical nature of polygons and the physical implications, suggesting a lack of connection between the two realms.
  • A question is raised about the continuity of dimensions of length and breadth, with some participants proposing that this continuity is a fundamental aspect of geometry.
  • Another participant challenges the assumption of physical continuity in space, noting the existence of both quantum and continuous space-time theories.
  • There is a suggestion that limiting the number of regular polygons would result in a geometry that cannot represent certain shapes, raising questions about the purpose of such a limitation.
  • Participants reiterate the idea that a finite number of regular polygons would impose restrictions on the types of polygons that can exist, leading to further speculation about the consequences of such a change.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mathematics and physics, with some agreeing on the implications of finite polygons while others question the assumptions of continuity in space. The discussion remains unresolved regarding the consequences of a finite series of regular polygons.

Contextual Notes

Participants have not fully explored the implications of their assumptions about continuity and the nature of space, leaving some questions about definitions and the scope of geometry unresolved.

Jackrell
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The two dimensional regular polygon series, the triangle, square, square, pentagon etc. is infinite. If for some reason, it was finite, what would our universe become? especially the dimensions of length and breadth.
 
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Your first sentence is in the realm of mathematics. The question is in the realm of physics. I don't see any real connection.
 
I guess my question should be - Why are the dimensions of length and breadth continuous?"
 
Jackrell said:
Why are the dimensions of length and breadth continuous?"
You assume that space is physically continuous. This is not a given. There are quantum space-time theories as well as continuous space-time theories. Math can handle both.
 
Jackrell said:
I guess my question should be - Why are the dimensions of length and breadth continuous?"

It's because that's part of the principle and concepts of geometry.
 
That is exactly my point. if geometry were changed so that the number of regular polygons was finite, is there any way to know what the result would be?
 
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It seems that you would have a limited form of geometry that cannot represent certain shapes. If you limit the number of regular polygons to only those with 3 and 4 sides then you cannot represent a pentagon and beyond. But what would be the point of that?
 
Jackrell said:
That is exactly my point. if geometry were changed so that the number of regular polygons was finite, is there any way to know what the result would be?

The result would be that you will have a limit on the number of sides that a polygon can have. And whatever results from that is also included in that result.
 

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