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Topic: "Graphical" Period
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Al Coons

Posts: 898
Registered: 12/4/04
"Graphical" Period
Posted: Mar 6, 1998 7:02 AM
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The period of the sine function is 2Pi.

When plotting in the Cartesian plane we "see" this happening because f(x) =
sin(x+2Pi). Visually we look for the shortest "period" in which the values of
the function repeat itself. Of course, the period of the sine function is no
different when working with Polar Coordinates. r(theta) = sin(theta + 2Pi).
However, as you know, the polar plot of sin TRACES THE SAME POINTS with a
"graphical period" of Pi. This seems important to me. For example,
scientists might certainly want to know how often an particle passes a
detector as it follows a circular track. Questions:

1) Is there a formal name for what I have called "The Graphical Period of a

2) While we all note this when we teach polar plotting, is there a formal
study of this idea and even general formulae which apply across a large range
of functions?

3) Is this idea as important as it seems to me in applied mathematics,
science, traffic control,....?

Thanks in advance,

Albert Coons, Ph.D.
Buckingham Browne & Nichols School
Gerry's Landing Road
Cambridge, MA 02138
(617) 547-6100

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