Electronic Proceedings of the Eighth Annual International Conference on Technology in Collegiate MathematicsHouston, Texas, November 1619, 1995Paper C031A Cupful of Limacons 
Michael L. TreudenDepartment of Mathematics and Computing University of WisconsinStevens Point Stevens Point, WI 544813897 USA Phone: (715) 3464607 m1treude@uwspmail.uwsp.edu 
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We suppose the unit disk x^2+y^2<=1 is the bottom of the cup and the sides are formed by revolving the graph of a smooth function x=f(z) with f(0)=1 and f'(z)>=0 about the zaxis. For example, f(z)=1 when the cup is a cylinder. A CAS such as Mathematica, for example, makes it easy to model the reflected light rays formally, without even specifying exactly what f(z) is. By then making particular choices for f(z), we may use the plotting capabilities a CAS provides to assess the accuracy of the model by comparing the graphs with what is seen in reality.
Keyword(s): computer algebra systems, Mathematica, geometry