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Variations on a Circle

 Activity Description Activity Guide

This activity has students write equations and draw circles using the Cartesian, parametric, and polar coordinate systems. It also asks students to explore translations and rotations of polygons.

Mathematics Topics: Students generate Cartesian, parametric and polar equations of circles. They also work with parametric equations to translate and rotate polygons generated from circles.

Mathematical Thinking: Students generate equations, connect equations and graphs, revise equations

Technology: Graphing calculators are used to draw parametric and polar graphs and trace points.

Sample Screenshots: Below are screenshots of: (1) circles generated from Cartesian, parametric and polar equations respectively, and (2) several polygons generated from altering the parametric equations and/or steps of the original circle.

Figure 1. A circle in three coordinate systems.

Figure 2. Three variations of the circle.

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