**by Margaret Trandel**

**The Beauty of Mathematics**

Polar Equations

This exploration is for my high school tutorial students who have not yet been exposed to polar equations. This is a tour of some beautiful mathematical graphs. To my students, I'd like you to simply relax, listen to the music(make sure the sound is on on your computer) and enjoy the tour. At the end there is a link available for more information on polar equations. If you put your TI-83 into polar mode, you can explore Polars on your own.

Enjoy as we take a tour of polar graphs including the graphs of some equations in the form r = a + b cos k (theta) such as**: r =** (1+ cos( theta)), (1+ 2 cos (theta)), (1+.5cos( theta)), (1+2cos2(theta)), (1+2cos(8theta)), (4 + cos(8 theta)) ,(6+cos8(theta)), (1+ 1 cos (1 theta)) , (1 + 1 cos(3 theta)), (1 + 1 cos( 10 theta)), (1 + 1 cos (1000 theta) (1+cos (500) theta), (1 + cos (30)theta).

Enjoy the beauty of mathematics as you take the following musical tour of polar equations!

Did you notice any patterns? I bet you have questions on how these graphs are created, such as what is r and what angle is theta? Follow this link to learn more about Polar Equations. Have fun creating some Polar Equations on your own!! E-mail me if you have any questions or want to discuss polar graphs! I hope you've enjoyed this activity!!! Mrs. Trandel