A Spiral of Squares

Here’s a little something I made yesterday for my precalculus class to try to make sense of.

Bezier Squares 8 Squares fastest

If you follow a single corner, you’ll see that it’s path is quite simple relative to the straight line it’s traveling along, if you’re able to ignore the fact that that line seems to itself be moving. The basic idea is that the point that is exactly 72% of the way from to q can be written as .72q + .28p. I made this in about 15 minutes in Geogebra, by using this method of writing points as “weighted averages” of other points over and over again. Check out Bezier Curves for more info, and thanks to my student Nico for teaching me about Bezier Curves!

Learning Objectives:

  • Parametrizing points in between p and using the form aq + (1-a)p where a is a number between 0 and 1.
  • Using Geogebra flexibly: “multiplying points by numbers.” [The word vector is lurking in the shadows.]
  • Learning to make rad GIFs using parametrics.