Question

For the Heisenburg uncertainty principle, where did the 4 pi come from in the equation, which is "x times p is greater than or equal to h divided from 4 pi"?

Answer 1

That factor appears when you actually do the quite complex maths that lead to the principle; it's quantum mechanics, and it's not something that can be shown easily.

What is important to note is that this factor $\frac{1}{4\pi}$is not important. What is important is that the uncertainty $\Delta x\Delta p_x$ is approximately of the order of $\hbar=\frac{h}{2\pi}$, which is a characteristic value that appears in many (most) formulas dealing with quantum mechanics.