Greenwood press

72
POLAR COORDINATES
The positions and distances on the globe are represented as a polar coordinate system. 

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Some spirals that can be graphed with polar coordinates model shapes in
nature. Note in the figure below how the shape of the spiral of the form 
r = ab
θ
mimics the shape of the shell of the chambered nautilus. As the creature grows,
the shell compartment expands in a way that allows the nautilus to retain its
shape.
Although polar coordinates simplify equations for some beautiful curves, they
also make some equations more complicated. For example, the polar equation for 
the line 
y = mx + b is r =
b
sin θ−m cos θ
.
Polar coordinates have surprising uses in computer graphics. The polar coor-
dinates distortion filter available for Adobe Photoshop remaps every pixel’s rec-
tangular (Cartesian) coordinates to polar coordinates, or vice versa. This makes
it easy to make objects circular as well as producing fountain-like effects associ-
ated with turning polar coordinates into Cartesian ones.