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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 Bearings

What on earth are polar coordinates, and why would you want to use them?

Polar Flower

Age 16 to 18 Challenge Level:

The point $P$ with polar coordinates $(r,\theta)$ is such that $OP=r$ and the angle between the x-axis and the line through $OP$ is $\theta$ measured counter clockwise. Equivalently if $P$ has Cartesian coordinates $(x,y)$ then $x=r\cos \theta$ and $y=r\sin \theta$.

The question asks for an explanation of the features of the graph. If you want to use a software package to sketch the graph you may want to download the shareware graphing software Graphmatica .