User:Nathan H. Douglas/sandbox

Hi! My name is Nathan H. Douglas. I like math. I also have theories about things, like the circumference of an ellipse.

Why must the circumference of an ellipse be $C\,=\,4a\int _{0}^{\pi /2}{\sqrt {1-e^{2}\sin ^{2}\theta }}\ d\theta \,=\,4a\,E(e)$, which has a freaking integral in it, and not just $C=2\pi \cdot \left({\frac {a+b}{2}}\right)$?

I don't know. But one thing's for sure.

I don't really know how to do Calculus. :>

I mean, I learned it, that's for sure, but I don't really understand it too well.

How do integrals work?

What are derivatives for?

What the heck does a limit do?

I understand the quadratic formula, though.

$x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}$, when $ax^{2}+bx+c=0$.

For example:

$3x^{2}+8x+5=0$

We can plug this into the formula and get $x={\frac {-8\pm {\sqrt {8^{2}-(4\cdot 3\cdot 5)}}}{2\cdot 3}}$

We can simplify: $x={\frac {-8\pm {\sqrt {64-60}}}{6}}$

We can simplify further: $x={\frac {-8\pm {\sqrt {4}}}{6}}$

Again:$x={\frac {-8\pm 2}{6}}$

This is the part where the answer diverges. The $\pm$ means there's two answers.

Final answers: $x={\frac {-6}{6}}$, which equals $-1$, OR $x={\frac {-10}{6}}$, which comes out to be $-1.{\overline {666}}$.

So yea.