# Math Help - Circumference of a Hypocycloid

1. ## Circumference of a Hypocycloid

Find the circumference of hypocycloid x^(2/3) + y^(2/3) = a^(2/3)

As per the question, I need to find the circumference of a hypocycloid. I had no idea what a hypocycloid was until about five minutes ago, nor even that such a thing existed, never mind finding the circumference of it... What the heck do I need to do here?

2. Originally Posted by Hellreaver
Find the circumference of hypocycloid x^(2/3) + y^(2/3) = a^(2/3)

As per the question, I need to find the circumference of a hypocycloid. I had no idea what a hypocycloid was until about five minutes ago, nor even that such a thing existed, never mind finding the circumference of it... What the heck do I need to do here?
Parametrise it by $x=a\cos^3\theta,\ y=a\sin^3\theta\ (0\leqslant\theta\leqslant2\pi)$. Then the length is $\int_0^{2\pi}\!\!\!\sqrt{\bigl(\tfrac{dx}{d\theta} \bigr)^2 + \bigl(\tfrac{dy}{d\theta}\bigr)^2}\,d\theta$.