The Arithmetic Properties of Circles

i imagine it's clear that we're not talking about real world utility, that this is for bitter curiosity. You just want to understand things about circles and the way they pack together for the fun ofit, right? That's right. I'm ok with that. But that's the kind of thing mathematicians like to do, yes? And then, you know, when you extend it to higher dimensions, it starts, you start thinking about bubbles and the formation of soap film, and and bubbling in general, and minimal surfaces. It turns into something that isn't necessarily just pure thought, in fact. So what we haven't gotinto at all is the the arithmetic properties of