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