The Significance of Pi: Is It Related to Spatial Dimensions?

[mjacobsca]

Is it possible that the value of Pi is related to the properties of the spatial dimensions of our universe? Could another universe with different properties see circles differently and arrive at a different value for Pi? After all, Pi is determined based on ratios determined within our own spatial dimensions, and from what I've read, some theories suggest that spatial dimensions may not manifest themselves the same throughout a multiverse. Like all the unexplainable constants I've read about in physics, perhaps Pi has deeper significance than just mathematics.

I don't want this thread closed for speculation. So I guess I'm asking whether such a topic has ever been proposed or even makes sense at all.

 

[DaveC426913]

Yes. It is possible in other geometries that the ratio of a circle's circumference to its diameter will not be the same as in our universe. You could have a universe whose dimensions are so small in extent that its curvature is noticeable. A circle's circumference would be measurably smaller than 3.141596 times its diameter.

 

[Chronos]

Pi in flat spacetime can be calculated using pythagorems's theorem, you just need to draw a bunch of triangles and calculate the hypotenuse. I actually did this once to about 50 decimal places before concluding it was merely an excruciating waste of time. I also discovered my computer was unable to accurately calculate beyond about 20 decimal places.

 

[mathman]

Pi is a number defined as the ratio of the circumference to the diameter of a circle in Euclidean (plane) geometry. It is therefore a mathematical concept, not a physical one.