Why is 4 ∏ in so many physics formulas?

[tucanaz]

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.

 

[ColinW]

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.

 

[sophiecentaur]

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.

 

[tucanaz]

Thanks very much, that makes sense...