Calculus: Visualizing z = (x^2 - y^2)/(x^2 + y^2).

The surface z = (x^2 - y^2)/(x^2 + y^2) has the simple equation z (r, t) = Cos (2 t) in cylindrical coordinates. The surface is therefore obtained by wrapping the graph of the curve z = Cos (2 t) on a circular cylinder and then expanding this cylinder in all directions.
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