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 $$C \,=\, 4a\int_0^{\pi/2}\sqrt {1 - e^2 \sin^2\theta}\ d\theta \,=\, 4 a \,E(e)$$, 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 $$x=\frac{-8\pm\sqrt{8^2-(4\cdot3\cdot5)}}{2\cdot3}$$

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

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

Again:$$x=\frac{-8\pm2}{6}$$

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.