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!