Is there a formula for cycloid?
My approximation is $((2\times(x\div(\pi\div2)))-(x\div(\pi\div2))^2)^.626$.
$$x = r \cos^{-1} \left(1 - \frac{y}{r}\right) - \sqrt{y(2r - y)}$$
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$$x = r \cos^{-1} \left(1 - \frac{y}{r}\right) - \sqrt{y(2r - y)}$$