Polar Gallery
The following is a gallery of demos for illustrating selected families of functions These figures and animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions for functions. Two file formats, gif and mov are available.
The gif animations should run on most systems and the file sizes are relatively small.
The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.)
The collection of animations in gif and mov format can be downloaded; see the 'bulk' zipped download category at the bottom of the following table.
We use abbreviations, GSP for Geometer's Sketch Pad 4, MAT for MATLAB, and EX for Excel spread sheet, to indicate the software used to generate the frames of the animation. If alternate corresponding software is also available there will be more than one abbreviation in that category.
Gallery of Animations
Other Selected Resources:
The book Exploring Conic Sections
with The Geometer's Sketchpad, by D. Scher, Key Curriculum Press,
Emeryville, Ca., 2002, is an excellent source of experiments involving
conic sections suitable for high school or mathematics education students
at the collegiate level. A cd is included.
At
http://www.math.odu.edu/cbii/calcanim/#polar is a collection of 8
animations of polar curves including spirals, rose
curves and limacons. As each curve is generated a table of values is
displayed.
At
http://www.geocities.com/xploremath/polarcoordinates/polarcoordinates.html
is a very nice applet for polar curves that has two sliders available for changing
values of parameters. There is a nice tutorial included for
exploring graphs of polar equations.
At
http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/polar.html
is a nice applet for polar graphs that displays as many as 5 functions of
the form r=f(θ).
Another
applet at
http://www.ies.co.jp/math/java/calc/sg_kyok/sg_kyok.html
will graph polar curves. This is available for purchase.
At
http://www.ies.co.jp/math/java/calc/graph_etoax/graph_etoax.html
is an excellent applet for the equiangular spiral that also displays area
information.
At
http://mathworld.wolfram.com/topics/PolarCurves.html
is a collection of polar curves which is part of Eric Weisstein's World of
Mathematics. Associated with each curve is a wealth of information.
At
http://wwwgroups.dcs.stand.ac.uk/~history/Java/index.html
is the
Famous
Curves Applet Index which contains applets to display polar curves as well
as many others.
Two other collections which have some interesting presentations of polar curves as well as others are http://curvebank.calstatela.edu/index/index.htm and http://www.2dcurves.com/index.html.
Credits:
Special thanks to Deane Arganbright of University of Tennessee at Martin and to Walter Hunter at Montgomery County Community College for their assistance with the development of the Excel files that accompany this gallery. The book "Mathematical Modeling with Excel", by Erich Neuwrith and Deane Arganbright (BrooksCole) provides a rich source of information for developing Excel routines for mathematical instruction.
Thanks to Mark Yates of The McCallie School for assistance in developing the Geometer's Sketchpad routines.
This gallery was developed by David R.
Hill, Temple University.
8/6/03DRH Last updated 5/22/2006 Since 8/29/03
