Pi

The gaussian distribution can be written as sinusoids.

idk man the taylor series for e^z can be decomposed into some sin and cos shit nigga

>>9044539
Fine. What about other, totally circle-unrelated equations, that have Pi in them... why is Pi there? What does Pi have to do with things that have nothing to do with circles?

>>9044531
>What does Pi have to do with things that have nothing to do with circles?
It might help if you gave some examples.

OP doesn't understand the gaussian integral

>>9044531
If π you see pi somewhere, then there is a circle "hiding". A circle is a very general and simple thing and you describe stuff using its concept very often, even without noticing it.
It's not that π is special, it's just that the circle is something really fundamental.

If you want to actually see where the circle hides in some specific example, then just read the proof and see how it pops up.

>>9044547
They do have to do with circles... because they can be represented with pi.

>>9044531
https://math.stackexchange.com/questions/904648/intuitive-reason-for-why-the-gaussian-integral-converges-to-the-square-root-of-p

https://www.youtube.com/watch?v=cTyPuZ9-JZ0

>>9044615
I'm not looking for a proof. I'm looking for intuition and deeper understanding of math.

I'd like to know why Pi pops up in so many, seemingly unrelated, equations.

>>9044628
It is because circles are everywhere. It's like one of the simplest things out there, like a straight line segment. That's why you see π everywhere.

If you can't get intuition from a proof, then you don't understand the proof well enough.

>>9044628
don't think of circles as in euclidian x and y, think of it as a relation between 2 variables

>>9044671
>don't think of circles as in euclidian x and y, think of it as a relation between 2 variables
Please expand anon. You seem to be a non-elitist and have some deeper insight. How does a relation of two variables end up as 'circles'?

>>9044687
The formula for a circle (at the origin) is x^2+y^2 = radius^2. This is a consequence of the Pythagorean theorem (it's the set of all possible points that have the property that they are exactly "radius" distance from the origin).

If your workings ever come across two variables squared, you can probably get a circle out of it.

Also you can show by Taylor Series that e^(ix)=cos(x)+i*sin(x), so you can work with circles from exponential functions, too.

>>9044782
very interesting. thanks!