What is the physcial signifcance of pi's appearance in a mathematical solution, if any?? Pi, the circumference of a circle divided by diameter, shows up in all sorts of mathematical solutions..classical, quantum, sometimes in unexpected mathematical results. As an example, Unruhs law is a simple equation giving the equivalent energy kT of a uniformly accelerating particle, as: kT = ha/ 2(pi)c (a quantum phenomena) Source: Wikipedia, http://en.wikipedia.org/wiki/Bill_Unruh I don't know how it was derived, so I don't know if pi was an input. Another example is in simple harmonic motion T= 2(pi) root(m/k) pi again!!!! (a simple classical formulation) In this case it likely arises as a result of formulation with trig functions and pi is used in the formulation and remains in the answer. Is pi always in the output because it was an input...in other words does pi become an element of an answer only because it was an element of the original equation? Or can it emerge without being an input...and when it does what physcial significance can we attribute to a constant with a geometric origin??