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.

1. The gif animations should run on most systems and the file sizes are relatively small. 

2. 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.) 

3. 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.

4. 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

Cardioids EX also a GSP file		Vary a: Gif Animation                Mov Animation Tracing:Gif Animation                Mov Animation
Rose Curves EX also a GSP file		Vary a: Gif Animation                Mov Animation Vary b: Gif Animation                Mov Animation Tracing: Gif Animation                 Mov Animation
Rose Curves EX also a GSP file		Vary a: Gif Animation                Mov Animation Vary b: Gif Animation                Mov Animation Tracing: Gif Animation                 Mov Animation
Lemniscates EX also a GSP file		Vary a: Gif Animation                Mov Animation
Limacons EX also a GSP file		Vary a: Gif Animation                Mov Animation Vary b: Gif Animation                Mov Animation
Equiangular Spiral EX also a GSP file		Vary a: Gif Animation                Mov Animation
Spiral of Archimedes EX also a GSP file		Vary a: Gif Animation                Mov Animation
Lituus EX		Vary a: Gif Animation                Mov Animation
Cochleoids EX		Vary a: Gif Animation                Mov Animation
Conic Sections EX also a GSP file		Vary k: Gif Animation                Mov Animation Vary e: Gif Animation                Mov Animation
Rose 'Style' Curves EX also a GSP file		Vary a: Gif Animation                Mov Animation
Zipped downloads ==>	Download (all) Gif and Mov animations  Download (14) Excel files  Download (9) Geometer's Sketch Pad files

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://www-groups.dcs.st-and.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 (Brooks-Cole) 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