While designing a computer laboratory exercise for my calculus students, I happened to sketch the curve defined by this vector equation: (x, y) = (cos(t), sin(t)) + 1/2(cos(7t), sin(7t)) + 1/3(sin(17t), cos(17t)). I was thinking of the curve traced by a particle on a wheel mounted on a wheel mounted on a wheel, each turning at a different rate. The first term represents the largest wheel, of radius 1, turning counter-clockwise at one radian per second. The second term represents a smaller wheel centered at the edge of the first, turning 7 times as fast. The third term is for the smallest wheel centered at the edge of the second, turning 17 times as fast as the first, clockwise and out of phase.
Wheels on Wheels on Wheels-Surprising SymmetryMathematics and Computer Science
PublisherMathematical Association of America (MAA)
Citation InformationFARRIS, Frank A. "Wheels on Wheels on Wheels-Surprising Symmetry."Mathematics Magazine 69, No. 3 (1996): 185-189.