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submitted 3 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

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[-] zkfcfbzr@lemmy.world 157 points 3 months ago* (last edited 3 months ago)

Kind of intentionally obtuse since they used eₑ as a variable and eₑₑ as another variable, and used (e-e) as an exponent a few times, which is basically the equivalent of multiplying by 1 in a fancy way. The first and last term also perfectly cancel out.

The same integral written in a saner form is:

integral from -e^e to e^e of (integral from -e^e to e^e of e^-(x^2+y^2)dy)dx

[-] xthexder@l.sw0.com 73 points 3 months ago

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 67 points 3 months ago

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 3 months ago

The approximation is only around 4.2810^-101 off from pi.
https://www.wolframalpha.com/input?i=integral+from+-a+to+a+of+%28integral+from+-a+to+a+of+e%5E-%28x%5E2%2By%5E2%29dy%29dx
https://www.wolframalpha.com/input?i=%281-erf%28e%5Ee%29%5E2%29pi

[-] kata1yst@sh.itjust.works 41 points 3 months ago

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 3 months ago* (last edited 3 months ago)

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

[-] daqu@feddit.org 7 points 3 months ago

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

[-] UnrepententProcrastinator@lemmy.ca 4 points 3 months ago

As an engineer, I approve this message!

[-] ulterno@lemmy.kde.social 0 points 3 months ago

My maths exam asked me to consider pi=5.

[-] vonxylofon@lemmy.world 1 points 3 months ago

"I will... consider it."

[-] bleistift2@sopuli.xyz 1 points 3 months ago* (last edited 3 months ago)

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

> quote

[-] xthexder@l.sw0.com 20 points 3 months ago* (last edited 3 months ago)

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 3 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.