Here's something that has been bugging me for decades. Well I keep forgetting about it thankfully, but I've never really been able to answer it. Why is Pi actually the value that we have for it and not some other number? If the ratio of a circle's circumference to its diameter was any different, then a regular hexagon wouldn't be composed of 6 equilateral triangles, but is there a fundamental reason why this had to be the case? I know that it can be generated with various series, so if we use that as an answer then the question becomes, why those series? I've mentioned this to a few people over the years and everyone just looks at me blankly or gives some kind of hand-wavey argument. It seems that there's only me that sees it as a valid question. To phrase this a different way, why does flat geometry have 6 equilateral triangles fitting the circle? This happens to be true in our everyday experience of nature, but were it not the case and we were to live in curved space would we consider that curved space to be 'flat' and other spaces curved relative to it? If so then why do we end up with a definition of a flat space with the very precise symmetry of the 6 equilateral triangles fitting the circle?