grav

2006-Jul-07, 01:30 AM

I have read that a non-Euclidean geometry can form triangles that are less or greater than 180 degrees and that the value for pi (more specifically, the ratio of the circumference of a circle to its diameter) can also change. This much is true. But I have also read that this may mean that our universe may be non-Euclidean and that the value for pi may be a result of this. In other words, if it were flat in this case, it might change to something else, perhaps exactly three. So the only reason it is not exactly three, then, would be because space is curved.

I have also read implications, including in this forum, that the value of pi might also change from one region of the universe to another. That somehow the space-time continuum curves differently for different regions, probably having something to do with the apparent curving of light through denser regions or something of this nature. I can demonstrate that pi is a universal constant and in a round-about way show implications that the universe is also flat.

If the value of pi changed even slightly from region to region in the universe, then the value that is obtained in any particular region becomes arbitrary. That is to say, it can have any value at all (but would depend, of course, upon the characteristics for that particular region). It might be three, or slightly greater, or much smaller. And it wouldn't just jump from value to value for different regions, but would change ever so gradually with the topography, so all possible values in between are accounted for, and pi can be represented by any number whatsoever depending on what region it is measured in, which makes it purely arbitrary.

Okay. So here's my argument. If the value of pi were a purely arbitrary number which depends on the topography of a region, then no true formula can be made to obtain its value. In other words, no regular pattern of calculations could be made that would exactly equal pi, so that its value can be found to billions of digits, which it is. The odds of the value of pi varying against this, then, is at least ten to the order of billions, which is tremendous. Many such formulas exist to find pi to any digit. This means that its value is not any arbitrary one, but very much a universal constant. This should also be the case for the universe in general, although it is much more difficult to explain, much less prove. But if my thinking is right, though, and pi is the ratio for a flat space or topography only, and it is a constant for the universe as a whole, then the universe should also be flat, otherwise pi would have some other arbitrary value that depends on its topography.

As far as I can see, the only argument that can be presented against this is the possibility that the value of pi as we know it is wrong. That is to say, the only true way to find the ratio of the circumference to the diameter is to actually measure them firsthand. To do this, we must first create a perfect circle somehow, and then a perfect measuring device. We assume with the formulas that we derive for pi that it will follow these formulas to the finest degree. So the billions of digits we produce by using these formulas is with the assumption that the value of pi follows the specific pattern by which the formulas are found, and that it does not vary in the slightest. I personally, however, believe this to be the case.

I have also read implications, including in this forum, that the value of pi might also change from one region of the universe to another. That somehow the space-time continuum curves differently for different regions, probably having something to do with the apparent curving of light through denser regions or something of this nature. I can demonstrate that pi is a universal constant and in a round-about way show implications that the universe is also flat.

If the value of pi changed even slightly from region to region in the universe, then the value that is obtained in any particular region becomes arbitrary. That is to say, it can have any value at all (but would depend, of course, upon the characteristics for that particular region). It might be three, or slightly greater, or much smaller. And it wouldn't just jump from value to value for different regions, but would change ever so gradually with the topography, so all possible values in between are accounted for, and pi can be represented by any number whatsoever depending on what region it is measured in, which makes it purely arbitrary.

Okay. So here's my argument. If the value of pi were a purely arbitrary number which depends on the topography of a region, then no true formula can be made to obtain its value. In other words, no regular pattern of calculations could be made that would exactly equal pi, so that its value can be found to billions of digits, which it is. The odds of the value of pi varying against this, then, is at least ten to the order of billions, which is tremendous. Many such formulas exist to find pi to any digit. This means that its value is not any arbitrary one, but very much a universal constant. This should also be the case for the universe in general, although it is much more difficult to explain, much less prove. But if my thinking is right, though, and pi is the ratio for a flat space or topography only, and it is a constant for the universe as a whole, then the universe should also be flat, otherwise pi would have some other arbitrary value that depends on its topography.

As far as I can see, the only argument that can be presented against this is the possibility that the value of pi as we know it is wrong. That is to say, the only true way to find the ratio of the circumference to the diameter is to actually measure them firsthand. To do this, we must first create a perfect circle somehow, and then a perfect measuring device. We assume with the formulas that we derive for pi that it will follow these formulas to the finest degree. So the billions of digits we produce by using these formulas is with the assumption that the value of pi follows the specific pattern by which the formulas are found, and that it does not vary in the slightest. I personally, however, believe this to be the case.