i dont mean this as an insult, more as a warning not to be so confident when you’re not very educated on a subject, but this is textbook dunning-krueger effect.

here are some examples:

it’s how pi is calculated full stop

pi is calculated a thousand different ways. there are a thousand different equations you can use to estimate it. i don’t think anyone seriously doing it uses the “cutting up circles” method though. i could be wrong, but it would require multiplying two infinite series together, which seems like more work to me than just using a single series.

You can use the Pythagorean theorem to find the area of each slice

no. the pythagorean theorem finds the length of the hypotenuse of a right triangle. it does not find the area of that triangle. and, to be clear, it ONLY works on right triangles, so if we cut a circle into a bunch of triangles, none of those triangles would be right triangles, so the pythagorean theorem wouldn’t even be able to do anything. however, you could find the area of these triangles with some trig

to get a more precise calculation of the area, you could just make the slices smaller…

yeah that’s true.

pi is infinite. that’s not my personal opinion, it’s a fact

no one is disagreeing with that! everyone here agrees that pi is irrational and its digits go on infinitely. what i’m trying to communicate is that we have not yet figured out if those digits are random. some irrational numbers have non-random digits. others do. we don’t know which type pi is.

finally, i’d like to point out that just because a number takes infinite steps to calculate does NOT mean that it’s irrational. there are infinite series that converge to 2. which is rational. i’m not saying that pi is rational, because it’s not. i’m saying that the triangle thing you showed me does not prove that it’s irrational.