Practice with polar coordinates provided an exciting opportunity to ground our thinking in space, not to mention virtual reality. We began with this problem:
In video games, images are drawn on the screen using x-y coordinates. The origin (0,0), is the lower-left corner of the screen. Mario moves from his position at (8,5) through a distance of 13 units along a line at an angle of 25º (measured against the x axis).
What are his new coordinates?
In his new position, how far is Mario from the origin (diagonally)?
Students should be able to use some basic trig to solve for Mario’s new position, and his distance from the origin. We then used this problem as an introduction to polar coordinates.
As practice, I had students locate the polar coordinates of objects in our own videogame landscape. The challenge was as follows:
Nora has been traveling through Mushroom Kingdom on her way to rescue Princess Toadstool. Unfortunately, she has lost a few things along the way! Help her find them again by identifying the location of the following items in POLAR COORDINATES (r, q).
1. Wrist watch 2. Glasses
3. Squeegee bottle 4. Coffee
5. Fried egg 6. Dance trophy
7. Boot 8. Earing (it’s quite small, but I think I left it in the jungle)
9. Venus fly trap (I always over-pack!) 10. Gold Coins
The problem was also a fun excuse to introduce the video work of Cory Arcangel. Arcangel is perhaps best known for his interventions with video game technology. You can see some of his videos here.