I'm currently in an intro chemistry class and a lot of the material is review from the multiple physics classes I have taken. Most of it comes back easily, including how to use the uncertainty principle to solve the small array of homework questions thrown at me but when trying to grasp a deeper understanding of the principle there is something I can't seem to figure out and it isn't mentioned in detail in the chemistry book. I understand, conceptually, that the closer the uncertainty of x gets to zero, the more the uncertainty of v would approach infinity but algebraically, i'm not sure how he came up with the formula, more specifically where he got the 4pi from. I recall from calculus that 4pi would be two rotations around a circle. This lead me to think that perhaps 4(pi) could be representative of the period of the wave exhibited by the particle--assuming the particle to have both particle and wavelike properties. If this were true, putting the period of the wave in the denominator (as it is in the uncertainty principle) would be equivalent to multiplying by the reciprocal of the period (the frequency). However the frequency would be unknown, would it not? So the period would have to be unknown as well. Here I go confusing myself again, i'll quit rambling now. In summary, where does the 4(pi) come from in the denominator of Heisenberg's uncertainty principle?