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submitted 1 month ago by [email protected] to c/[email protected]

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[–] [email protected] 67 points 1 month 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.

[–] [email protected] 31 points 1 month ago (1 children)

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 41 points 1 month 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.

[–] [email protected] 14 points 1 month ago* (last edited 1 month ago)

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

[–] [email protected] 7 points 1 month ago (2 children)

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

[–] [email protected] 4 points 1 month ago

As an engineer, I approve this message!

[–] [email protected] 0 points 1 month ago (1 children)

My maths exam asked me to consider pi=5.

[–] [email protected] 1 points 1 month ago

"I will... consider it."

[–] [email protected] 1 points 1 month ago* (last edited 1 month ago)

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

> quote

[–] [email protected] 20 points 1 month ago* (last edited 1 month 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.

[–] [email protected] 9 points 1 month 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 5 points 1 month ago

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