this post was submitted on 17 Jul 2024
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[–] xthexder@l.sw0.com 71 points 4 months ago (1 children)

Wait... that's not an approximation at all! That equals exactly pi. If I understand the math correctly, it's effectively a formula for the area of a unit circle.

[–] OrganicMustard@lemmy.world 66 points 4 months ago (3 children)

That should be an approximation. To get exactly pi the range of both integrals should be from minus infinity to infinity like this. It's the integral of the 2D Gaussian, which is fairly known.

[–] cryoistalline@lemmy.ml 31 points 4 months ago (1 children)
[–] kata1yst@sh.itjust.works 41 points 4 months ago (3 children)

And because it always bears repeating;

According to JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman-

Let's go to the largest size there is: the known universe. The radius of the universe is about 46 billion light years. Now let me ask (and answer!) a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient.

[–] jlh@lemmy.jlh.name 14 points 4 months ago* (last edited 4 months ago)

Technically you need another 20 digits if you want to get down to a Planck length. (57 digits in total)

[–] daqu 7 points 4 months ago (2 children)

So the number 3 should be close enough for home use. Good to know. Thanks!

As an engineer, I approve this message!

[–] ulterno@lemmy.kde.social 0 points 4 months ago (1 children)

My maths exam asked me to consider pi=5.

[–] vonxylofon@lemmy.world 1 points 4 months ago

"I will... consider it."

[–] bleistift2@sopuli.xyz 1 points 4 months ago* (last edited 4 months ago)

You can quote with the “greater than” sign (>). Backticks mark text as source code.

> quote

[–] xthexder@l.sw0.com 19 points 4 months ago* (last edited 4 months ago) (1 children)

Ah, you're right. I was thrown off by WolframAlpha saying the integral = π ≈ 3.1416 Both of those should be ≈

(x^2 + y^2)=1 is the equation for a unit circle, so it's definitely related. Just not quite how I thought.

[–] OrganicMustard@lemmy.world 9 points 4 months ago

Also the 2D gaussian integral is used to give an insight on why the 1D gaussian integral is sqrt of pi. Here is a video with cool visualization for anyone interested.

[–] WolfLink@sh.itjust.works 5 points 4 months ago

“Fix” it with Lim as eee-> infinity (where eee is some other e-named variable)