Instead of beginning with definitions, theorems and worked examples of problems, this unit begins with an exploration. Students use a graphing utility to enter many parametric equations and, from their observations, make generalizations about parametric curves. The class accesses a lab with twenty Macintosh computers. The software available is Xfunctions, with its parametric graphing utility. With limited instruction the students are able to enter the equations correctly, as well as change the bounds of the parameter and minimums and maximums for the viewing window.
Students investigate a previously unknown topic in mathematics, parametric equations.
They develop their ideas on this topic by observing the behavior of many graphs of parametric equations. To conclude the introductory investigation, students prepare a summary of their findings to share with the class. Thanks to Dr. Wilson, I give students the first eight problems from EMT 668 assignment ten. Click here to view the problems. Students present their findings in various formats.