A wonderful coincidence or an expected connection: why π² ≈ g

Comments

• lvxferre@mander.xyz ⁨1⁩ ⁨year⁩ ago

  TL;DR: the old definition of the meter was based on the length of a string necessary to make a pendulum oscillate once each 2s. And since the oscillation of a pendulum depends on both gravity and π, by assigning that length the value of one unit, you end with gravity as π².

  This gets easier to see if you actually include the units into the equation:

  T = 2π√(l/g) // the formula for pendulum oscillation
  T² = 4π²l/g // getting rid of square roots, bloody roots
  g = 4π²l/T² // same junk as above, just reorganised
  g = 4π²l/(2s)² // pendulum oscillation arbitrarily chosen to be 2s
  g = π²l/s² // cancelling out 4 and 2²
  g = π²(1m)/s² // "we shall call that length ONE METRE!"
  g = π²m/s² // gravity is pi times pi, plus typical accel unit
  

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