I found this formula for the circumference of an ellipse:
$$4aE(e)$$
where
$$e = \sqrt{1-\frac{b^2}{a^2}}$$
and
$$E(x) = \int_{0}^{\pi/2}\sqrt{1-x^2\sin^2\theta}\;d\theta$$
$a$ is the semi-major axis (or, in other words, the maximum radius), and $b$ is the semi-minor axis (minimum radius).
Now somehow, this is related to $2\pi r$ for the circumference of a circle.
Is there an easier way to find the circumference of an ellipse than to do this integral? Because I can't do integrals yet.
I can do square roots, but not integrals; and square roots in integrals are even harder than integrals themselves. Okay, so, technically, I can do integrals, but only the antiderivative kind of integral.
In other words I could do this:
$$\int x = x^2$$
But a definite integral is one of the kinds I can't do.
So, is there a way that I can more easily find the circumference of an ellipse? Would I need to know the circle it could have come from and that circumference and then scale that circle circumference by whatever factor made the circle an ellipse?