On pi:
Pi and all irrational numbers ARE special, because they do not exist in physical space. You cannot split an object, or a space, into "pi". At whatever decimal you decide that it is close enough to pi, it is just that; not pi, just close enough, a bit more or a bit less.
On numbers in general:
What is the nature of a number? Does "being 1", "being 2", "being 7.64" really exist? When there is "one" object on a table, how is the fact that there "is one" real?. It's like saying an object "is bigger than" another. What exactly is the nature of such a relation? Just food for thought, nothing very practical.
On nothing and quantum physics:
(Quantum) physicists now have crazy theories about "vacuum energy" and whatnot now, there is no true nothingness but only "vacuum in average" or something like that. Matter and energy can pop into existence and disappear just as quickly, as long as everything is kept on average. I don't really know what to think of all that, like "what about the space between atomic nuclei and electrons?"...
Speaking of which, electrons don't spin around atomic nuclei like planets around stars, they just have a high chance of being somewhere around nuclei... these clouds of probability (called orbitals) can indeed be spherical, but also pear-shaped, or somewhere in between, and their shape, size and positions are determined by some precise factors (the Periodic table is built to classify elements based on the properties their electronic configurations give them). Or at least that's how physics/molecular chemistry understands it (and teaches it) as of now.