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Polar Bearings
Age 16 to 18
Challenge Level 
The article Where? Over There... introduces polar coordinates, so it might be useful to read it through to help you to get started on this problem.
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Maltese Cross
Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.
Polar Flower
This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.