Exploring Some Polar Graphs with Sketchpad

I really like the new version 5 of Geometer’s Sketchpad. One of the most useful new features is the ability to quickly create parameters that can change over a specified range continuously or in specified jumps. Then you can use those parameters in functions that can be plotted. In the screencast below, I used parameters and animation to illustrate properties of some special polar graphs, specifically “rose curves”, cardioids, limaçons, and lemniscates:


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