Plotting an animated hypocycloid I want to animate a Hypocycloid using computer code. So far i have drawn the circles here. I have found this definition on wikipedia and I want to animate the image that is on the right. I did something similar here with a sine wave. I used a counter and changed the position of the shapes using `cos` and `sin` to plot the changing shapes on each change of the counter. This new graph is infinitely more complicated. Wikipedia gives the following equations: $x(\theta) = (R - r) \cos \theta + r \cos((k - 1) \theta)$ $y(\theta) = (R - r) \sin \theta - r \sin((k - 1) \theta)$ I do not know how to solve these equations. Why is it $x(\theta) = $ and not just $x =$ ? How do I find $\theta$ when it occurs on both sides of the equation ; besides, I do not understand what $k$ is.

You misunderstand the meaning of $x(\theta)$. The parentheses do not indicate multiplication; they instead indicate that $x$ is a **function** of the parameter $\theta$. To plot this curve for a given $R$, $r$, and $k$, all you need to do is plug in various values of $\theta$ into each equation on the RHS, and the first equation gives you the $x$-coordinate and the second gives you the $y$-coordinate.