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Dr. Paul Chabot
Department of Mathematics
California State Univ.,
Los Angeles

Polar Graphs

Create Your Own Polar Animations Using Maple!

 The graphics in this deposit were created using Maple software

NCB Deposit  # 29

A Sampler for the Student.  To view a larger continuous animation, click on the image in each cell.

This is a large file with many graphics that may require several seconds to load.
The above animations are the polar graphs of . . .

The middle image takes the equation from polar form to rectangular coordinates.

### Dr. Chabot's Maple Work Sheets can be easily altered to graph any polar function on any domain.  [Only one line of code for each change.]  The instructions are in the Work Sheets linked on the left.  The provision is that you must own a copy of Maple.

These polar graphs have the shape of a petalled flower.  They were named  Rhondonea in the 18th century by the Italian mathematician Guido Grandi.  Today we call this a Rose polar graph.

In our equation,  n =  4, an even number.  If n is even, the Rose will have  2n petals.  If n is odd, the rose will have the odd number of n-petals.

 Shikin, Eugene V.,  Handbook and Atlas of Curves, CRC Press, 1995, pp. 304-306. Yates, R. C.,  Curves and their Properties, NCTM, 1952.  Also in A Handbook on Curves and their Properties, various publishers including the NCTM. Weisstein, Eric. W.,  CRC Concise Encyclopedia of MATHEMATICS, Chapman & Hall/ CRC, 2nd ed., 2003. For Mathematica® code that will create polar graphs:      Gray, A.,  MODERN DIFFERENTIAL GEOMETRYof Curves and Surfaces with Mathematica®,    2nd. ed., CRC Press, 1998. < http://mathworld.wolfram.com/Rose.html >