When a circle of radius [math]r[/math] rolls inside a circle of radius [math]R > r[/math], then a fixed point on the rolling circle[br]traces a curve called a [i]hypocycloid[/i].[br][br]Experment with the interactive illustration below. In particular, study the special cases:[br][br][math]\frac{R}{r} = 2[/math] (the resulting curve is a segment of a straight line);[br][math]\frac{R}{r}= 3[/math] (the resulting curve is called a deltoid);[br] [math]\frac{R}{r} = 4[/math] (the resulting curve is called an asteroid).