The two dimensional regular polygons.

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The discussion centers on the implications of limiting the series of two-dimensional regular polygons, such as triangles and squares, to a finite number. It raises the question of how this limitation would affect the dimensions of length and breadth in our universe. The conversation highlights the distinction between mathematical concepts and physical realities, particularly questioning the continuity of space. While some argue that the continuity of dimensions is a fundamental aspect of geometry, others suggest that if geometry were restricted to a finite set of polygons, it would result in a limited geometric framework incapable of representing more complex shapes like pentagons. This limitation could fundamentally alter our understanding of geometry and its application in physics, leading to a constrained view of spatial dimensions.
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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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