A year ago I decided to see if fifth graders could create shapes using polar coordinates. I bet myself that they could if we spent some time first traversing a polar grid, identifying the labels of the rings and the spokes. We didn’t think of them as angles and radii, because those semantics weren’t important to us. We just needed a mechanism for addressing locations on the grid.
I looked around on the internet for a polar graph paper that the students could draw on, but I wasn’t satisfied with my options. Few had labels, and I dreaded the prospect of adding them in by hand. An algorithm—not me—would be the appropriate laborer. To Twoville I turned and produced this graph:
Who needs a collection of 100 different versions of polar grid paper when you can have just one expressed parametrically?
The fifth graders managed just fine.