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

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Using Restrictions in Innovative Ways

Let’s talk restrictions.  So helpful, so amazing.  I’ve seen people use restrictions in some very creative ways lately, so here’s the lowdown on cool ways to use restrictions.  Make sure to scroll to the end to see an Angry Birds activity that makes extensive use of restrictions.

First, the classic use: restricting x and/or y.

You can restrict just the x values, or you can restrict just the y-values, or you can stack restrictions.  Desmos even knows the difference between AND and OR:

Here, I’ve shown a graph with x > 0 OR y > 0
In Desmos, type the restrictions in the same bracket, separated by a comma: {x>0,y>0}

BTW, this is super helpful if you want to do something like this:

Restriction by List 2

Here, I’ve shown a graph with x > 0 AND y > 0
In Desmos, type the restrictions in separate brackets: {x>0} {y>0}

The team at Desmos has also made it possible to place restrictions on both x and y at the same time in an implicitly defined inequality.  Here is one example:

Link to Desmos: see how this is done!

Second: restricting parameters.  This allows certain aspects of the graph appear or disappear depending on a certain parameter.  It also can be used to make whole images appear or disappear.  Here are some of my favorite examples lately:

Here I built upon a graph that Desmos had featured, and set it up to turn on tangents by sliding a point on the graph.  This technique is awesome for building teacher activities where you want to make a graph into an interactive exhibit (i.e. students can’t access the expression list, just the  graph itself.)  Check out the graph here.

For another example, here is a tweet by Stefan Fritz showing a fantastic Angry Birds activity he created that gives students feedback as they work through the clever use of restrictions on parameters.  Here’s the link to the teacher activity for anyone who wants to use it!  Such a fun activity!