Polar Coordinate Stickers
One of my first jobs out of college was teaching AP Calculus BC. Since polar coordinates made such beautiful designs, we created stickers from the graphs of their equations. Then, I asked students to analyze and then explain why their sticker looked the way it did.
I also asked the students to put the sticker somewhere they would see it every day before the AP exam, perhaps on a water bottle or laptop, and to remind themselves of the mathematical reasons that it looks that way. I also asked them to explain why the equations look the way the do to their friends who saw the sticker. It really helped reinforce polar coordinates.
Here are the steps we followed:
Go to desmos — an epic graphing calculator and more website.
1. Start by typing in a sin(theta) or cos(theta) equation to create a circle.
2. Scale the radius by multiplying your trigonometric number by a value.
3. Okay, here’s where it gets crazy with the limaçon {snail in French}. The explanations here can get really lengthy. It is cool, though, to have the students start to understand how the values differ between the angles of 0 and pi and then 0 and 2pi.
4. The grand finale: changing the argument of the trigonometric function that makes the limaçon repeat many times, creating the petals.
Then you need to just turn the grid off in desmos, take a screenshot, convert the file to dxf, and load it into Cricut Design Space or Silhouette Studio, depending on your cutting machine.
