Science Memes

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submitted 2 months ago by [email protected] to c/[email protected]

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[–] [email protected] 71 points 2 months ago (12 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.

[–] [email protected] 65 points 2 months ago (11 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] 20 points 2 months ago* (last edited 2 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.

[–] [email protected] 9 points 2 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.

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