Comment by ValentinA23
1 year ago
Only because you're using metric seconds instead of "imperial seconds" (the time it takes for a 1 foot long pendulum to complete a full oscillation).
1 year ago
Only because you're using metric seconds instead of "imperial seconds" (the time it takes for a 1 foot long pendulum to complete a full oscillation).
Sure, if you change either of the units you can always change the other one to fix the equation again.
But does it work when you use the right Imperial technique?
If I come up with my own measuring unit, let's call it the sneezle (whatever the actual length I assign to it) I will be able to also define a duration unit (say, the snifflebeat) based on the time it takes for a pendulum one sneezle long to complete a full oscillation, and vice versa I can define the sneezle by adjusting the length of a pendulum so that it oscillates in two snifflebeats. Here are the maths:
T = 2π√(l/g)
T/2π = √(l/g)
(T/2π)^2=l/g
g = l/(T/2π)^2
g = l/(T^2/4π^2) = 4π^2xl/T^2
Now substitue T with 2 and l with 1 an you get
g = 4π^2x1/2^2 = π^2
It doesn't matter what the pair of units assigned to T and l are. However, they'll be interrelated.
There is nothing arbitrary, and no coincidences behind g =~ π^2. It just requires to do some history of metrology and some basic maths/physics.
If you want to discuss coincidences, may I suggest you to comment on this remark I made and which hasn't received any attention yet ?
https://news.ycombinator.com/item?id=41209612
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