Best Witches!!

/ ivasallay / Leave a comment

I designed a self correcting domain/range project for students. The object of the project is to restrict the domain or range of each line that makes up the tangram witch below so that the witch is outlined in yellow.

When finished, the witch will look like this:

There is more than one combination of ways to limit the domains or ranges of the lines making up the witch, but the witch above is NOT one of them. Copying it will not complete the assignment.

I’m sure you can complete the first witch by limiting the domains or ranges of each line, so do give it a try!

Happy Independence Day!!

/ ivasallay / Leave a comment

This morning in my neighborhood, I enjoyed a better-than-I-could-have-imagined 4th of July parade of decorated bikes, scooters, and wagons, followed by a light breakfast. When I got home, the thought of making this flag in Desmos popped into my head, so here is the result:

If you would like to see the equations I used to make the flag, click here, but be warned: depending on your device, the image might have disproportionate stars and stripes. I made it on an iPhone, so it should look good on your phone.

However, if you are reading this blog post on your phone, this next image will NOT look great, but if you are reading it on a desktop or an iPad, you should be able to enjoy watching the flag wave beautifully with fairly good proportions.

If you are reading this on your phone, click here, and the proportions of the waving flag should be better.

I hope you have a very lovely Independence Day!

 

Happy Fathers’ Day!!!

/ ivasallay / Leave a comment

I created a bowtie for Fathers’ Day with just 5 expressions in Desmos Plaid, but the only way I can share what it looks like on my blog is to take a screenshot of it. You can also see it by clicking here.

How did I know how to make a tie in Desmos? I watched a YouTube video that does a nice job of explaining some of the math behind the bowtie.

If the bowtie is not viewed in Desmos Plaid, this is what it looks like:

So even if things don’t turn out exactly the way you would like, I still wish a very Happy Father’s Day to all the fathers out there and to everyone who has a father in their life they love. ♥♥♥

An Amazing Whip

/ ivasallay / 2 Comments

I was playing around in Desmos with some functions/relations and sliders, and some of them made me think about a whip, specifically Indiana Jones’s bullwhip. I decided to find a silhouette of Indiana Jones, trace it in Desmos, and put one of the whips in his hands. Here’s the result:

The MANY bullwhips used in the Indiana Jones movies ranged in length from 6 to 16 feet, so it doesn’t bother me at all that the one I created constantly changes length.

Here’s a compilation video of some of the many ways that Indiana Jones used his bullwhip.

The first Indiana Jones film premiered forty-five years ago today, on June 12, 1981, so I think this is the perfect day to share my Desmos bullwhip with you!

Happy Mothers’ Day!!!

/ ivasallay / Leave a comment

I decided to create a flower in Desmos for all the wonderful women who have mothered children at any time in any way. Here’s what I made.

The leaves were actually more complicated for me than the flower. My sister likes a lighter shade of pink, so I lightened the color:

Then I imagined it would be cool if the flower’s color changed. Here is the flower with bright, changing colors:

And if you prefer the lighter colors:

Which flower color choice do you like best? Have a very happy Mothers’ Day!

 

Hoppy Easter!

/ ivasallay / Leave a comment

I made this bunny for Easter in Desmos. Is it one bunny with a shirt and eggs that magically change colors, or is it a succession of bunnies hopping over the lawn ready to hide eggs?

Happy Hoppy Easter, everyone!

Peeps and Eggs

/ ivasallay / Leave a comment

Peeps are in stores everywhere at Eastertime. They come in many different colors and flavors, as well as in several not-to-be-eaten forms. I decided to make some peeps in Desmos and add some painted eggs for good measure. I’ve never seen green peeps before, but there will be green ones here.

I hope you find the best treats this year.

 

We’re Approaching Pi Day!

/ ivasallay / 3 Comments

It’s almost Pi Day, so I made this in Desmos:

Here it is again, but without the pies rotating:


All four of my pies are calorie-free but rather tasteless. If you’re looking for a Pi Day pie to make your mouth water, try https://www.outerbanksvoice.com/2026/03/02/happy-pi-day-2/

Some people like writing poems about pi, like this one by Cindy Bousquet that I found in the comments on this post.

Mathequalslove has several Pi Day logic puzzles and games for you to enjoy as well.

With Pi, the fun never ends!

 

 

Cat Rotating Around a Bouncing Ball

/ ivasallay / Leave a comment

Not every topic in my mathematics education was covered equally well. I don’t recall learning anything about geometric transformations when I was in school. Many years after I graduated from college, when I was teaching mathematics, I learned how to make a shape rotate around the origin:

For each original point (x, y),
(-y, x) maps it 90° counterclockwise around the origin,
(y, -x) maps it 90° clockwise around the origin, and
(-x, -y) maps it 180° around the origin.

This year, the 9th-graders I work with at school need to know how to rotate a shape around a point that is NOT the origin. This is a topic I had never thought about before. To patch up this hole in my math knowledge, I decided to play with rotations in Desmos.

I began with
the point (-1, 2) and
the endpoints (2, 3) and (4, 7), and
the polygon function in Desmos to connect the endpoints.

I noticed that the point and the line segment had the same relationship as
(0, 0) and
the line segment with endpoints (3, 1) and (5, 5).
I noted that the following coordinates worked beautifully to rotate the line segment:
(x-1, y+2) maps it onto the line segment’s original endpoints, (2, 3) and (4, 7).
(-y-1, x+2) maps it 90° counterclockwise around (-1, 2),
(y-1, -x+2) maps it 90° clockwise around (-1, 2), and
(-x-1, -y+2) maps it 180° around (-1, 2).

I was quite pleased with the symmetry of those relationships, so I decided to add a few more ordered pairs to my table in Desmos: (4,-3), (6, 3), and (-2, 4). Desmos’s polygon function automatically rotated the line segments produced by those ordered pairs, and this lovely symmetrical design was produced:

Next, I wondered what would happen if I changed the center of rotation. I made an ordered pair, (a, b) and used sliders to move the point around. Now the point reminded me of a ball, and I got the idea to make the rotated shape look like a cat playing with the ball. I made the original cat a little darker than the rotated ones. This was the result:

That cat took a lot of ordered pairs to make. I got to thinking about how rotations are often used in tessellations. I found a simpler-looking kitten that tessellates and recreated it in this Desmos graph. Again, the original cat is darker than the rotated ones.

No cats were harmed in the production of these graphs.

Which of the cats do you like the best, or would you have used a different animal to play with the ball?