The two dimensional regular polygons.

[Jackrell]

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.

 

[mathman]

Your first sentence is in the realm of mathematics. The question is in the realm of physics. I don't see any real connection.

 

[Jackrell]

I guess my question should be - Why are the dimensions of length and breadth continuous?"

 

[out of whack]

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.

 

[Kenny_L]

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.

 

[Jackrell]

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?

 

[out of whack]

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?

 

[Kenny_L]

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.