Envelope of a diameter by a complete rotation of a wheel

M. Jamet
Area of the Envelope of a diameter or a radius by a complete rotation of a wheel. All curves are cycloids, the upper ones obviously, but also the lower smaller ones wich was more of a surprise (to me). It turns out that the lower cycloids are the caustics of one of the upper one, thus no light is involved. To see that effect, check this animation about the caustic of the cycloid: http://www.geogebra.org/m/2626429 Thanks a lot to mathcurve.com for the idea with the caustic! start the animation!