Changing the Domain of Polar Graphs

In today’s post: a work-around for specifying the domain of a polar functions. (hint: it involves a quick switch to parametric equations.)

What’s your favorite type of equation? I have always loved polar equations, but in the last year or so, parametric equations have taken polar’s place as #1.  This post may help to explain one of the reasons behind my change of heart.

Graphing polar functions is super fun. The curves polar functions generate are fun and unexpected. And when you graph them on Desmos, they’re simply stunning. But as of right now, you cannot specify the domain of a polar function on Desmos.  As far as I can tell, it will only draw polar graphs for values of θ from 0 to 12π radians:Polar Spiral

This suffices for many basic graphs, but even in the case of this spiral, it means that we aren’t seeing the whole picture.  For example, what happens when θ is negative? What about for larger values of θ? Continue reading

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My Favorite Thing

It’s coming up on one year since I launched this blog, and in honor of the #MTBoSblogsplosion, I’m actually writing my 2nd post just this week.  It’s fitting that the prompt is “My Favorite Thing,” because that’s literally what this entire blog is all about.

I mean, don’t get me wrong, I have more than one favorite thing. I like cooking, baking, dancing, singing, mathing, drinking tea, breathing in the springtime air as the ground is just thawing.  I have lots of favorite things.

But ask my students what my favorite thing is and they will all, without hesitation, tell you it’s Desmos.  They’ve all come to expect that on Fridays I wear Desmos shirts.  And they pretty much think I spend all my free time playing on Desmos.  They also all know how to sing the Desmos song I wrote.  Well, it’s more of a “jingle.”  You can sing it too!  Here’s how you do it.  You sing in the highest note you can, with the most enthusiasm possible “Des-mooooos!”*

Adults also know Desmos is my favorite, but they’re skeptics and require some winning over (which usually just consists of them actually trying it). This fall I was fortunate enough to be a part of Desmos’s first ever Teacher Fellowship Cohort, where I had the opportunity to go out to Desmos HQ in San Francisco. People warned me: make sure it’s not like a time-share, where they’re just trying to sell you something. There are also people who think I’m just promoting Desmos so much because I must be getting something out of it.

Honey, please.

Desmos didn’t come find me. I sought them out. Continue reading

Illustrating Volumes of Solids with Known Cross Sections

My posts are few and far between these days.  I hope that changes soon, but for now, it’s just a post here and there when I can.  And today I can!  Let me share some fun Desmos-ing with you!

cross-sections-2

In this post:

  • A new Desmos feature: how to use labels!  
  • Attending to the clarity and usability of graphs.  
  • Fun cross-sectional solids graphs to play with!!  What could be better?

It’s no secret with my colleagues that I love Desmos.  For real. SO. MUCH.  And I love it when people ask me to help them look for Desmos graphs or activities for particular topics.

Which brings us to today. One of the calculus teachers I work with was asking me about whether I knew of any good Desmos graphs of rotational solids.  I sent him some awesome graphs made by Geoff Patterson.  Graphs that use such advanced math that my jaw drops with awe.  Seriously.  If you haven’t given his blog a look, do yourself a favor and check it out.  Pronto. Here’s a link: http://www.geoffofx.com/.

 

732203_orig
This picture is of one of Geoff Patterson’s creations. Image can be found at http://www.geoffofx.com/uploads/1/5/8/9/15895202/732203_orig.png

But what I didn’t know Continue reading