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Math Help - Circumference of a Hypocycloid

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    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?
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    Quote Originally Posted by Hellreaver View Post
    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.
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