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Math Help - Astroid

  1. #1
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    Astroid

    x(t) = (a cos^3 t, a sin^3 t), where a is a positive constant, traces a curve known as an astroid. Wikipedia gave me a sketch of the curve, but is there an intuitive reason why it's possible to draw an approximated sketch of the curve just based on the formula?

    Also, how can I calculate the total length of the curve? Is it just the regular formula for arclength where t is between -1 and 1?

    Thanks!
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  2. #2
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    \int_{-1}^{1}\sqrt{(dx/dt)^2+(dy/dt)^2}dt
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