Happy Fathers’ Day!!!
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
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!!!
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!
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
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!
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
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?
2026 Math Facts and Factors
In this blog post, I’m sharing as many math facts about the number 2026 as I can find on my own or shared by others on Bluesky. I’m publishing the post before the year ends, but I will add additional number facts after the new year begins as well.
Countdown to 2026:
Here’s a countdown you can use right before midnight on New Year’s Eve:
make misc GIFs like this at MakeaGif
Here’s another countdown I saw on Bluesky:
Here’s another nerdy & numerical New Year countdown I came across! This time, for the upcoming 2026. Enjoy using this for the upcoming year! :3 #Mathematics #MathSky #MathChat #MathsChat #NewYearCountdown #NewYear2026
— Math Nerd 1729 (@mathnerd1729.bsky.social) December 18, 2025 at 4:50 PM
If you have any problem seeing the 2026 video, here is a screenshot of its final frame.
Factors of 2026:
- 2026 is a composite number.
- Prime factorization: 2026 = 2 × 1013.
- 2026 has no exponents greater than 1 in its prime factorization, so √2026 cannot be simplified.
- The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying, we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore, 2026 has exactly four factors.
- The factors of 2026 are outlined with their factor pair partners in the graphic below.
What Kind of Shape is 2026 in?
2026 can’t claim a shape of its own, but it does have a relationship with some other numbers that can.
2026 is one more cube than the sum of the cubes from 1 to 9.
1³ + 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³ = 2026.
2026 is the sum of three perfect squares in several different ways.
45² + 1² = 2026, so it’s shaped like this: 
(You can click on images to see them better. Each of the 2026 cells is numbered.)
2(23² + 22²) = 2026. Since it’s double the sum of consecutive squares, it’s also shaped like this:
Since 2026 = (2(22) + 1)² +1, it is also one more than the 22nd centered octagonal number.
2026 is also the sum of three triangular numbers in 31 different ways:
Changing from 2025 to 2026:
Happy New Year everyone!
— Isokon Gallery (@isokongallery.bsky.social) December 31, 2025 at 6:30 PM
Yes, 2026 is one more than 2025, or in the case of this video, 2026 is one more car than 2025.
2025 🔜 2026
— 🍁🇨🇦Team Canada Forever🇨🇦🍁 (@teamcanadaforever.bsky.social) December 28, 2025 at 4:40 PM
And in a brilliant post on Bluesky, 2026 is one more billiard ball than 2025.
Some “Powerful” Facts About the Number 2026:
Since 2026 is the sum of an even number of consecutive numbers,
505 + 506 + 507 + 508 = 2026, we get this “powerful fact”:
508² – 507² + 506² – 505² = 2026.
45² + 1² = 2026, so
(3² + 6²)² + 1² = 2026.
2026 would be a palindrome in base 13 and in base 45:
11(13²)+12(13¹)+11(13º) = 2026.
1(45²) + 0(45¹) + 1(45°) = 2026.
2026 is in exactly two Pythagorean triples:
90-2024-2026, and
2026-1026168-1026170.
On October 24, 2026, we can celebrate the Pythagorean triple,
10-24-26.
I’ll finish off this topic with a “powerful” math joke about 2026:
The Revolutionary Discovery That 2026 Equals 2026
#Math #Exponents #Tautology #Obvious #2026
https://sciencehumor.io/math-memes/the-revolutionary-discovery-that-2026-equals-2026-terq
— ScienceHumor.io (@sciencehumor-io.bsky.social) December 28, 2025 at 7:41 PM
2026 in Complex Numbers
2026 is the sum of two squares, 45² + 1², therefore it is the product of two complex numbers. If you are logged into Bluesky, you can see that complex product in the following post:
Here are two other complex number facts involving the number 2026:
2026 Games and Puzzles
Math=Love has mazes and other puzzles featuring the number 2026.
2026 is divisible by 2, but not by 4, so it is the magic sum of a magic square puzzle, specifically the one that uses the numbers from 499 to 514.
Happy 2026!
Here’s when 2026 starts around the world! It’s that time of year again, and we can play the 2026 NCTM Year Game in our January lessons. Use the digits in the year 2026 and the operations +, −, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), along with grouping symbols to…
— Colleen Young (@colleenyoung.bsky.social) December 31, 2025 at 6:00 PM
Peter Rowlet reports on Bluesky that the 2026 game works for the numbers 1 to 10 but doesn’t spoil your fun.
MathGames has also shared some 2026 fun facts and games.
Among other mathematical facts about the number 2026, Scientific American’s reprint of Spektrum der Wissenschaft’s Why 2026 Is a Mathematically Special Number informs us that the 8-magnetic-disk version of the mathematical game, Tower of Hanoi, will always take at least 2026 moves to solve.
More About the Number 2026:
0 + 12 × 34 × 5 – 6 – 7 + 8 – 9 = 2026. You can find another count-up equation on the MathGames blog.
2026 degrees is 1013π/90 radians.
If you are logged into Bluesky, you can see The Maths Bazaar’s post informing us that
2026 = 2¹¹ – 2 × 11,
2026 = √(2²²) – 22, and
that each of the following is a prime number:
2026 + 1,
2 + 0 × 26 + 1,
20 × 26 + 1,
202 × 6 + 1.
2026 = √(2²²) – 22 inspired me to make a graphic for it and some other equations I had already found:
Mathometry has some suggestions for math activities involving the number 2026.
From this Bluesky post and its link to OEIS, I learned that there are “2026 hyperforests spanning 10 unlabeled nodes without isolated vertices.”
2026
https://mathr.co.uk/web/2026.html
#math #mathematics
— The Mathematician (@math.blaze.email) January 1, 2026 at 11:10 AM
May 2026 be a delightful year for you and yours!
Saying Goodbye to 2025
You probably have an opinion on what kind of year 2025 was. Regardless of that, 2025 will always be a fabulous number. I wrote a post about 2025 that had so many number facts/puzzles from X and Bluesky that WordPress wouldn’t allow me to add or subtract even one word! That post is broken. You can read it, but I can’t edit it at all.
For my post welcoming 2026, I am only going to include math facts/puzzles I find on Bluesky, along with my own graphics. It will likely be a shorter post, but I’m confident I won’t break WordPress this time.
So, as we say goodbye to the complicated year 2025, I’d like you to know that 2025° simplifies nicely to 45π/4 in radians. Also remember that
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)² = 45² = 2025², and
1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³ = 2025.
Have a lovely time saying Goodbye to 2025!