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Why is 4 ∏ in so many physics formulas?

  1. Jan 27, 2012 #1
    I don't understand why 4 ∏ is in so many physics formulas.

    For instance, Heisenberg's uncertainty uses h / 4∏.

    Or Coulomb's law for the electric force

    Or the formula for the Magnetic permeability of free space:

    Many formulas use 4 ∏ or 8 ∏. I just don't understand why the relationship between a circle's diameter and its circumference comes into play so much.

    I am sure there is a simple explanation I am just not seeing.
  2. jcsd
  3. Jan 27, 2012 #2
    The surface area of a sphere is 4.pi.r^2 so anything that is spreading uniformly from a point source will tend to have that in there somewhere.
  4. Jan 27, 2012 #3


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    Π is one of those constants that show a basic spatial relationship where there is spherical symmetry and an isotropic space. e is similar in that it is a basic constant involving natural variations (decay and growth) in a linear time frame.

    The two constants are not constants once space and time stop being uniform.
  5. Jan 28, 2012 #4
    Thanks very much, that makes sense...
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