Fourier Plaything
Imagine: Around the sun rotates the earth (Let's pretend a circular orbit with sun at the center). Around the earth rotates the moon (Again let's pretend...). Around the moon rotates a... house (We're allowed to imagine, right?). Around that house rotates a space dog. Around that dog rotates a cosmic flea. And so on.
From the fixed perspective of the sun, what's the shape of the path traced out by the smallest rotating object? Find out by playing with the sliders in this construction.
This would be fun to study during a unit of high school or college trigonometry while hinting at the more advanced study of Fourier Analysis. Alternately one could choose to just play with the parameters and enjoying the geometry without even having to think too hard.
This construction is based on a Flash file I found at http://toxicdump.org/stuff/FourierToy.swf
In turn I found that after stumbling upon a fascinating article "The Math Trick Behind MP3s, JPEGs, and Homer Simpson's Face
http://nautil.us/blog/the-math-trick-behind-mp3s-jpegs-and-homer-simpsons-face