I see your points, and I acknowledge that my statements were not sufficiently thought out.
I know that the Universe seems to have a non-Euclidian geometry, and–indeed–we don’t know if length, width, depth, or volume has any meaning for anything “smaller” (if “smaller” has any meaning) than the Planck scale.
Indeed, we may never need to know Pi beyond about 35 digits, because if we know the exact diameter of the Universe, then calculating the circumfrence with Pi to about 35 digits will mean that we are “off” by less than the Planck scale (about 10^-35 meters).
If the Universe does have a non-Euclidian geometry, then the Pythagorean Theorem may not give the mathematical results that we think it will under certian circumstances . . . which I view as being similar to the difference between Newtonian (or “classical”) physics, and physics that take Relativity into account.
Even so, the theorem works on a flat surface . . . except that the Universe is not flat.
And we know that Pi has an infinite number of digits, so–by definition–it is unending.
Of course we can express Pi in other ways, but we can never know the number with perfect accuracy.
The most accurate value of Pi at the time of this writing is about 31.4 trillion places, which is probably more accuracy than anyone will ever need.