Is Pi more than just a ratio for circles? Is there a easy way to understand the universality of Pi?
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Saying that pi is ‘only’ related to the circle is downplaying things a bit, because circles are very important and simple mathematical objects that turn up *everywhere*. Any kind of repeating sequence, a *cycle* can be described with a circle somehow and pi will sneak in there, which is why it comes up a lot in physics, where waves are cyclical and waves are also *everywhere*.
Anything that rotates necessary pulls pi in because rotation happens in circular arcs.
The idea of a circle also generalises to spheres in higher dimensions, which gives pi opportunities to sneak in there too.
Sometimes pi sneaks in to seemingly unrelated places because a problem is converted into one that is solved using circles.
Can you describe a place that pi turns up where you can’t see the connection to the circle?
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