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
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.
The approximation is only around 4.28*10^-101 off from pi.
https://www.wolframalpha.com/input?i=integral+from+-a+to+a+of+(integral+from+-a+to+a+of+e^-(x^2%2By^2)dy)dx
https://www.wolframalpha.com/input?i=(1-erf(e^e)^2)*pi
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.
When did dolphins learn calculus?
it ends in deeedee so maybe this is dexter when his sister has used the mosquito-izer on him and he’s angrily yelling at her
This is a fantastic metaphor for what tinnitus feels like.
