Des-blog

The Friday Fave would like to tel youl about a very handy calculator feature, and then invite you to do some math.

The feature first.

Imagine you’ve got a set of points, and you’ve named them A, B, C, and D. You probably want to make a quadrilateral from those four points, and it used to be difficult but now it is easy.

What sort of thing is a quadrilateral? Why, it’s a polygon. So you just tell the Desmos calculator that you want to make a polygon with those four points, and boom!

Alternatively, you may have specified the x-coordinates of your quadrilateral with a list, and the y-coordinates with another. Do not ask the Fave how the calculator can interpret two lists just as easily as it can interpret four points, but it can.

This second version of polygon is especially handy because you can operate on a list (you cannot yet operate on points except by dragging them around). So now let’s do a little math together, shall we?

What do you suppose our polygon will look like if we type polygon(X,Y-4)? Click through on the expression to find out.

What about polygon(2X,Y)?

And finally, what will polygon(Y,X) look like?

Bonus question: What transformation do you need to apply to make our polygon no longer be a kite, and how might we express that transformation algebraically?

Now that the Fave has you thinking about polygons, here are some delightful ways to extend your thinking…

Polygraph: Advanced Quadrilaterals

Polygraph: Basic Quadrilaterals

Polygraph: Hexagons

Polygraph: Hexagons, Part 2

• The personified Friday Fave is a figment of the imagination.
  
• The Friday Fave posts every Friday without fail.
  
• The Friday Fave seeks to help you, Dear Reader, find new and wonderful things for your students.
  

Two of these statements are true, and one is a lie.

When the truths and lies are about people or fictional constructs, you can’t really know which is a lie unless you know the person or construct very very well.

But mathematical truths and lies are different. The evidence for veracity or mendacity is right there in the math. If you don’t know it, you can figure it out! This makes Two Truths and a Lie fertile ground for mathematical concept development; especially if

For months, Desmos has had some secret-not-ready-for-public-use Two Truths and a Lie activities, and now we’ve polished several of these and put them on display in the searchable activities at teacher.desmos.com

We have versions of this activity for each of these function types: Conics, Exponentials, Parabolas, and Linears (all true; no lies!). They are Challenge Creator based, so the differentiation is built right in—your students are telling the truths and the lies, as well as determining exactly which conic (or exponential or line) they’ll lie about.

The Friday Fave (who missed last week’s post, and so now you know the lie) encourages you to click on through and give these Two Truths and Lie activities a try.

It is gray outside the Friday Fave’s window as autumn begins in earnest. The Fave is left craving color and joy and beauty.

Fortunately, the Fave has a prescription—for Des-art. And now you do, too.

Maybe your art will take the form of curve tracing of a background image. The following examples, and many more, are waiting to inspire you at desmos.com/art

Or perhaps you’ll go a different route and create beauty from pure abstraction.

Many more examples of abstract art live at desmos.com/math

Finally, you may possibly find your artistic medium in images that are placed in calculated ways. Shelley Carranza built this beauty with a single teal square and a whole bunch of math.

She added a white square to the mix to make this one.

And finally, she used three images artfully arranged to make this gorgeous pattern.

Whether you are doing art to liven a gray autumn day, or using it as an invitation to mathematics for your students, Des-art—in all its many forms—may just become your Friday Fave every day of the week!