You can't make a perfect circle in the physical universe. And because of
quantum effects, no matter how close of an approximation you made, you could
never prove just how close it was or derive more than a few dozen
digits of pi from it, because it's impossible to measure distances smaller than
the Planck length.
Beyond that, quantum uncertainty dominates to to the point that smaller
distances are meaningless.
The Planck length is approx 1.6 x
10-35 meters, so a one meter as-perfect-as-possible circle might give
you almost 35 digits of pi, if you could construct such a
circle and if you could measure it with sufficient accuracy--both are
far beyond our current technology.
The observable universe has a radius of
about 4.4 x 1026 meters. So even in theory, the largest possible
physical circle you could construct (and you couldn't construct it because of
light-speed limitations) would only give you about 26+35=61 digits of pi. About
five dozen--less than a hundred. And that's using the entire universe!
:)
So, no, you can't just measure it. Pi is an abstract mathematical
concept without any meaningful physical reality. Pi has way more than
61 digits! --- Do not meddle in the affairs of Wizards, for it makes
them soggy and hard to light. [ Reply to This | Parent | # ]
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