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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.
Please be patient!
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 npetals.

Shikin, Eugene V., Handbook
and Atlas of Curves, CRC Press, 1995, pp. 304306.
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
>

