4.1. LINEAR MAPPINGS 415 θ r P y x Figure 4.1: Polar Coordinates as a mapping It is also possible (and, as we shall see, useful) to think of a system of one or more equations in several variables as a single equation involving a mapping: for example, the system of two equations in three unknowns b x 2 + y 2 + z 2 = 1 x + y − z = 0 which geometrically represents the intersection of the unit sphere with the plane x + y = z can also be thought of as ±nding a “level set” for the
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