A Sampler for the Student. To view a larger continuous animation, click on the image in each cell.
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This is a large file with many graphics that may require several seconds to load.  |
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. |