Hypocycloid
A hypocycloid is traced by a fixed point on a circle of radius r rolling around the inside of a circle of radius R. Use the slider to adjust the ratio R/r – this controls the shape of the curve. If R/r is an integer, the curve will have R/r cusps. The hypocycloid is a special case of the hypotrochoid.
Special cases are a line segment when R/r = 2, a deltoid when R/r = 3, and an asteroid when R/r = 4. See if you can figure out the connection with non-integer values of R/r and the number of cusps.
Move the slider to adjust the value of t to see the curve traced out - you can also click the play button in the lower left to animate.
To change the viewing window, hold the shift button and left-click to drag the graph or use the scroll wheel to zoom in/out. You can also adjust the axes by holding the shift button and left-click on the axis you want to change.