A hypocycloid is generated by the tracing a fixed point on a circle in which that circle rolls along the inside edge of the larger circle. I took some time to create a few of my own hypocycloid's using a GeoGebra software. My artistic side kind of got the better of me when doing this exercise as the numerous shapes and designs that could be created were intriguing.
Cardano, a man of many interests of the 16th century, studied hypocycloid's which later became known as Cardano circles. The construction of high speed printing presses were based off of these circular patterns. It would be interesting to see how hypocycloid's and even cycloid's are incorporated in to everyday life. I am sure the engineering world has a lot of use for these designs, but would rather see them as a mechanical curve instead of just a geometrical circle.
Link to Geogebra tool i used: http://www.geogebratube.org/material/show/id/29389