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Re: Gravity and pi



I have no historical records to support this hypothesis, but ...

One reasonable standard of length is a pendulum which swings from one
side to the other in 1.0 s (i.e. T = 2 s). This length has all the
hallmarks of a good standard: consistent, easily reproducible and
accurate (at least within the historical setting of the 1700's). If
this length is numerically equal to 1.0, then g is numerically equal to
pi^2!

g = T^2 L /4 pi^2

Perhaps part of the motivation behind choosing 10^7 m = (the distance
from the pole to the equator) was that it coincided nicely with this
existing standard. Then the coincidence is that the circumference of
the earth is exactly 40,000 km, not that g = pi^2.

Make of this what you will.


Tim