Tracing Parametrics, Chains of Events, and Constructing a Pentagon

Last week I attended a PD session by Suzanne Gaskell, an art teacher at the high school where I teach.  She presented on a work of art she has created and calls the Kavad of a Sacred Geometer.

This work of art is a wooden box that tells the story of ancient geometry and its relation to various sacred traditions.  After her presentation, she instructed us on how to perform some interesting constructions, including one I had never done before, the regular pentagon.

It inspired me to create an illustration of the construction for a regular polygon using Desmos.  Here’s what I came up with:

Pentagon Construction

TWO GREAT SKILLS I LEARNED

First skill: how to trace a parametric curve.  Prior to creating this, I didn’t know how to make a parametric curve trace itself out.  Here’s how to do it: Continue reading

Rotating a Function

You can pretty easily use parametric equations to rotate a function through any angle of rotation.

  1.  Define a function, f(x)
  2. Either choose an angle measure, a, or leave a as a slider and type in this parametric equation: (t·cos f(t)·sin a, t·sin a+f(t)·cos a)
  3. You’ll need to specify the values of t.  I generally use -20 to 20, because that will cover what is visible in a normal zoom.  If you want to zoom out quite a bit, though, you may want larger values as your bounds on t.
  4. If you want to animate the rotation, specify the bounds on the slider a.

Check out this example!  Click on the Continue reading

The Symmetry of Functions

As I work with students to analyze graphs, I’ve noticed that many of them have trouble distinguishing whether a function is symmetric about the y-axis or the origin.

I designed this activity to animate the reflection of a function about the y-axis and the rotation of a function about the origin.  I chose to illustrate symmetry about the origin as a 180° rotation rather than a reflection through the point (0,0).  I think this is easier for the students to learn to visualize in their minds.

To rotate the curve, I defined the rotation using parametric equations.  Desmos has a great learning demo on parametrics here

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Here’s my activity:

Symmetry Activity

Feel free to duplicate it and try editing it to something useful for your classes!  (Remember, if you just click preview, you won’t be able to see anything in a hidden folder.  You’ll see it just like the kids will.)