Apr

27

 What is it about square roots that they are so prevalent in natural phenomena? Gravity diminishes as the square root of distance. Tsunamis travel at the square root of the depth of the water. Energy is mass time speed of light squared. Why is this? Is it just a mathematical convention for ease of computation, and if so, why do natural phenomena follow this relationship?

Henrik Andersson suggests:

Sound, gravity and waves are propagating like surface of an expanding sphere. The surface of a sphere is 4*pi*r^2 (squared distance from the center). Thus the square is a result of the two-dimensional property of a surface.


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