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CARTESIAN COORDINATES
11
The position of Chicago on the earth
according to its latitude and longitudinal
positions, which are the same as the cen-
tral angles from the center of the earth.

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(34,118) to approximately (0.5934,2.0595). Using this formula, the distance be-
tween Chicago and Los Angeles is 
d = 3963 arccos[sin(0.7156) sin(0.5934)+
cos(0.7156) cos(0.5934) cos(2.0595 − 1.5184)],
which is approximately 1,758 miles.
online sources for further exploration
Celestial coordinates
html>
Creating an image map


Georeferencing and digital images
html>
The satellite times

Spherical coordinates and the GPS
coordinates/learn.htm>
Stereograms

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CIRCLES
Circles are used in many real-world applications. All manholes are round so
that their covers never slip through the pipes from the ground to the sewers. Any
way you turn the cover it is impossible to force it through the hole, since the dis-
tance from the center of the circle is always the same. Since polygons do not hold
this property, a circle is very useful for this purpose. 
Circular wheels allow the opportunity for constant and smooth motion when
riding a bicycle or automobile. If the circle had edges or vertices the ride would
become very bumpy, because the distance from the center of the wheel to its
perimeter would no longer be constant. In addition, a car will travel the distance
its wheels rotate, because the friction between the wheel and pavement cause the
car to move. For every revolution the tires make, the car will travel the length of