Friday, June 20, 2014

A Tool For Exploring Transformation Rules

Using the fantastic Desmos graph and their API, I made a little environment to explore transformation rules. (Click here!) The app let's you type in a rule that determines the transformation and then visualizes the image for you.

Part of the fun of playing with this -- for me, at least -- is exploring a wider set of transformation rules than I'm used to visualizing. 

love the idea of putting this in front of my geometry students next year before we study transformations. I think they'll have a lot of fun playing around with this. The other thing that I like about this app is that it provides a ton of Daily Desmos-style transformation problems.

Can you find a transformation rule that produces this image?

Can you find a transformation rule that produces this one? 

If you can find a rule for the rotation in that last picture, then give me ten minutes and I can explain what complex numbers are. Which is actually why I started to make this thing in the first place.

Enjoy! Let me know if you find bugs or think of improvements.

A huge thank you to the tremendous and brilliant Chris Lusto for helping me out throughout this project, and thank you to equally awesome Andrew Knauft for inspiring this project with his own work and for offering some crucial feedback and aid. These are good, generous people.


  1. 1. This is awesome. I will use this next year with my students.

    2. I need to learn how to use this api. Good project for the next few days.

    3. I teach 8th grade, and I really like introducing transformations -- visualizing them, recognizing them, exploring their properties -- before introducing motion rules. I guess I should just add this to my list of things to explore in the API, but is it possible to create buttons in order to perform and analyze transformations separately from the motion rules? For instance, here is an applet from Mr. Butler via Geogebratube that doesn't use motion rules, but isn't nearly as user-friendly as your Desmos graph. Thoughts?

    1. I think that this sounds doable. I like to have a question for kids in mind when I make these things, though. What could the challenge be for a kid using the sort of transformation environment you're envisioning?

  2. Your tool is great! I started messing with it a bit, in particular trying to get it to fit with a lesson from CPM Core Connections Course 3 (6.2.4) where the kids have to work out a transformation to go from a rectangle at {(-2,-2), (-2,-4), (-6, -4), (-6,-2)} to a rectangle at {(2,-2), (2,6), (6,6), (6,-2)} as a way to justify that the two shapes are similar. However, I have a long way to go before I can implement this myself in Desmos! Wondering if anyone would be interested in helping? Would also be great for the kids to be able to enter multiple transformations (steps) using arrow notation as a means of working up to a single transformation. I love how you have implemented using "arrow notation" btw!