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"Graphical" Period
Posted:
Mar 6, 1998 7:02 AM


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 Function?"
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. alcoons@aol.com Buckingham Browne & Nichols School Gerry's Landing Road Cambridge, MA 02138 (617) 5476100
Editor Technical Tips, "The Mathematics Teacher" AP Statistics Web Site: www.bbns.org/us/math/ap_stats



