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Hipocicloids e Hipotrochoids

Hipocicloids, [;r,R >0;] e [; \omega=\frac{R-r}{r} ;]: [; \underline{\textbf{r}}(t) = \begin{pmatrix} (R+r)\cos{t}+r \cos{\omega t}\\ (R+r)\sin{t}-r \sin{\omega t}\\ \end{pmatrix}, \quad t \in \mathbb{R} ;] Hipotrocoids, [; r,R >0, b \in \mathbb{R};]: [; \underline{\textbf{r}}(t) = \begin{pmatrix} (R+r)\cos{t}+(r+b) \cos{\omega t}\\ (R+r)\sin{t}-(r+b) \sin{\omega t}\\ \end{pmatrix}, \quad t \in \mathbb{R} ;]

Desenhe os Hipocicloids para [;R=1;] e [;r=3,2,1,1/2,1/3;]
Desenhe os Hipotrocoids para [;R=1=;], [;r=3,2,1,1/2,1/3;] e [;b=3,2,1,1/2,1/3,0,-1/3,-1/2,-1,-2,-3;].

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