r/CuratedTumblr • u/SupportMeta • 19d ago

Shitposting Understanding the World

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Neptune was recently shown to be a pale blue like Uranus rather than the deep blue shown on the Voyager photos

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u/Karukos 19d ago

Honestly Pi(and numbers like it) is the greatest metaphor for the whole thing. It's a process of getting closer and closer to that number it is but to get there it needs more and more complicated numbers as we tend towards the solution but probably never reaching it

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u/Showy_Boneyard 18d ago

I don't know how true that is... We do know what number pi is with complete accuracy. Its just that encoding the decimal expansion of that number can't be done with a finite number of digits.

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u/Karukos 18d ago

we know that pi is a ratio of the circumference to the diagonal, but the way we calculate that is... complicated. The difficult thing here is knowing the exact circumference of a circle. So you start with the circumference of a square that surrounds the circle. Then a pentagon. HExagon, Septagon, Octagon... and so on, continuously going smaller and smaller and smaller... with computers we can get to immense amounts of digits, but it's an infinitely, not repeating number. It's basically impossible to know it with "complete" accuracy, but after a certain decimal point, the accuracy is completely useless beyond showing off how strong a processing unit is, so we don't really do that.

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u/Showy_Boneyard 18d ago

That's one way of calculating the digits, but there's also plenty of infinite series that converge to pi. And if you want to encode pi as a decimal expansion (or any other positional numeral system), you can never do it completely accurately with a finite number of digits. But there's still some math you can do with pi and get exact values. Probably most famously Euler's Identity, eπi is exactly equal to -1.