ASTROID

This astroid is the set of points \( (x,y)\in\mathbb R^2 \) such that \[ |x|^\frac{2}{3}+|y|^\frac{2}{3}-1.8=0,\quad -3\le x\le 3,\ -3\le y\le 3. \]

generated with pstricks

The astroid is a roulette curve: If a small circle of radius \( r>0 \) rolls around the inside of a larger circle of radius \( R>r, \) then a point \( P \) attached to the small circle traces a hypotrochoid curve. The special case \( 4r=R \) generates an astroid.

generated with pstricks, 720 frames