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!
No Two Snowflakes are Alike
I was inspired by this post from Paddy MacMahon that I saw on Bluesky.
#MathsToday #ALevelMaths #FurtherMaths
Find the exact area of the snowflake.
— Paddy MacMahon (@paddymacmahon.com) December 23, 2025 at 8:19 AM
I loved that he produced this lovely snowflake from just one equation,
r = 16 + 6sin6θ + 4cos36θ. Wow!
Obviously, he knows a lot about polar coordinates, much more than I do, but that can’t keep me from playing around with his equation in Desmos and learning a little bit more in the process! All I did was replace the constant and the coefficients with sliders. My efforts produced these two snowflakes…
…and many more!
Then I thought, “What if I change the coefficients of theta?” I quickly learned that those coefficients need to be multiples of 6 to maintain the snowflake’s 6-sided shape, but yep, I’m learning from experimentation! I varied the theta coefficients over three equations to get this 3-D look:
It all makes me smile and think, “Let it snow! Let it snow! Let it snow!”
If you’re dreaming of a white Christmas, I hope you get the real thing, but if not, I hope these snowflakes will delight you at least a little bit.
Eight Desmos Ornaments
I made some Christmas ornaments in Desmos that I hope you will enjoy. If you click on and off the circles on the left of the descriptions, you can see all eight ornaments in one Desmos graph, or you can find them all pictured below in this post. If you click the arrow next to each description in Desmos, you can also see the equations used to produce each ornament. However, the snowflake and Rudolf’s face required many ordered pairs, which I put into a separate folder.
1. Decorated half red and half green:
2. Decorated with diagonal stripes:
3. Decorated with sines and secants:
4. Decorated with a snowflake:
5. Decorated with a checkerboard design: (This was a pleasant surprise that required only one equation!)
6. Decorated with a spiral
7. Decorated with ellipses for a 3D look:
8. Decorated with Rudolf’s face:
Perhaps you will choose to make an ornament yourself in Desmos. If so, I’d love to see it.
I hope you all have a very merry Christmas!
Trick or Treat?
I’m not much of an artist, but I still like playing around in Desmos. Here’s what I made this week. Have a Happy Halloween!
2025 Factors and Facts
Check back every now and then. As I find new facts about the number 2025, I’ll add them.
Countdown to 2025:
make science GIFs like this at MakeaGif
Math up your countdown to 2025…
= (10×9×8×7÷6÷5×4+3)×(2+1)
= (10+(9+8×7)×6)×5+4×3×2+1
= (10+(9×(8−(7−6×5))))×(4×3)+2-1+0!
= 10×(9+8×7−6+5!+4!)−3×2+1
= 10×9×(8+7+6)+5!+4×3+2+1
= (10+9)×(8+7+6)×5+4!+3+2+1#HappyNewYear#HappyNewYear2025 pic.twitter.com/BH4Jz2MbLX— Maths Ed (@MathsEdIdeas) December 31, 2024
The number 2025 is special:-
1) It’s a perfect square (45×45 = 2025) which comes after 89 years, the last was 1936.
2) It’s product of two perfect square, 9² × 5² = 2025.
3) It’s sum of three perfect squares, 40² + 20² + 5² = 2025.
May this year brings happiness & success! pic.twitter.com/maiRd0t5Th
— Radha Mohan (@RADHAMOHANKUNWA) January 1, 2025
Fun with the Digits of 2025:
The countdown to 2025 is on! I’ve been having so much fun making 2025-themed puzzles the last few weeks. It’s time to start sharing them!
2025 Square Edge Matching Puzzle
mathequalslove.net/yearly-squar…
#mtbos #iteachmath #edusky #mathsky #puzzlingclassroom
— Sarah Carter (@mathequalslove.bsky.social) December 26, 2024 at 8:37 AM
Start the New Year with a fun #math challenge! 🎉🧊 Break the ice with your students using the 2025 Year Game.
How many expressions can you and your students create from the numbers 1 to 100—using only the digits in 2025? Try it now: nctm.link/LvN1e
— NCTM (@nctm.org) December 26, 2024 at 6:23 AM
Happy New Year folks! 🥳
Share your own fun facts about the number 2025 😌 pic.twitter.com/xthCAwghC1— Andrzej Kukla (@Mathinity_) December 31, 2024
2024 was the year of the dragon, next year -is- the dragon
— Odendo (@odendo.bsky.social) December 22, 2024 at 1:18 PM
Factors of 2025:
Unless you were born before the end of 1936, 2025 will be the only year in your lifetime with exactly 15 factors.
- 2025 is a composite number.
- Prime factorization: 2025 = 3 × 3 × 3 × 3 × 5 × 5, which can be written 1458 = 3⁴ × 5².
- Since its prime factorization only contains even powers, 2025 is a perfect square. √2025 =
- The exponents in the prime factorization are 4 and 2. Adding one to each exponent and multiplying, we get (4 + 1)(2 + 1) = 5 × 3 = 15. Therefore, 2025 has exactly 15 factors.
- The factors of 2025 are outlined with their factor pair partners in the graphic below.
Here’s another way to display the factor pairs of 2025, although several are outside the visible gridlines.
Let’s continue the countdown to 2025.
Today’s 2025 Factor Tree Puzzle was inspired by Dr. Harold Reiter who presented on factor tree puzzles at a math teachers’ circle workshop I attended.
mathequalslove.net/2025-factor-…
#mtbos #iteachmath #puzzlingclassroom #mathsky #edusky
— Sarah Carter (@mathequalslove.bsky.social) December 27, 2024 at 8:14 AM
Happy New Year! The prime number decomposition of 2025 is super-cool: the first 5 numbers co-operate in an elegant fashion. I think it’s going to be a good year!
🥳🥂🔥❤️ pic.twitter.com/SM7Keoekrf— Edward Frenkel (@edfrenkel) December 31, 2024
Square Facts About 2025:
For the past few years, I’ve created a list of number facts about the year’s number. Here’s the 2025 version.
2025 is an odd composite number composed of two prime numbers multiplied together (3 × 3 × 3 × 3 × 5 x 5 or 3^4 x 5^2)
2025 is written as MMXXV in Roman numerals.
— Thomas Pitts (@ThomasJPitts) December 31, 2024
2025
=45²
={9(9+1)/2}²
=1³+2³+3³+4³+5³+6³+7³+8³+9³— taiga@cozy studio (@nico_taiga) January 1, 2025
Writing 1 once, 2 twice, 3 three times, and so on, up to 45 forty-five times [or (20+25) (20+25) times], produces a string of 2025 or 45² [or (20+25)²] digits — the only number where this happens. #HappyNewYear2025 • https://t.co/MALfH2q9yi pic.twitter.com/NJBXcrLz9Y
— Maths Ed (@MathsEdIdeas) December 28, 2024
2025 is going to be a really square year, and also be on the lookout for this specific square date!
#math #ITeachMath #EduSky
youtube.com/shorts/CEZ6B...
— Howie Hua (@howiehua.bsky.social) December 29, 2024 at 8:02 AM
This morning I learned that 2025 will be the first 'perfect square' year (45x45) since 1936 (44x44) and there won't be another until 2116 (46x46). Expressed in month/day/year format, there will be a total of 8 'perfect square dates' in 2025 (ex. 1/09/2025 ➡️ 1092025 ➡️ 1045x1045).
— Andrew in New Jersey (@aannddrreeww.bsky.social) November 19, 2024 at 9:38 AM
A classic proof without words showing that 1+3+5+...+(2n-1)=n² taking advantage of the fact that 2025 is a square and therefore it's the sum of all odd numbers from 1 to 89!#MathArt #Mathematics #HappyNewYear
Made with #python #matplotlib pic.twitter.com/uwpnBnRbwH
— Simone Conradi (find me in BlueSky) (@S_Conradi) December 31, 2024
2025 is …
a perfect square 45 x 45 = 2025.
a sum of cubes: 1³ + 2³ + 3³ + ... + 9³ = 2025
a perfect square when you add 1 to each digit:
3136 = 56²
a perfect square when you increase the first digit by 1:
3025 = 55²
Maybe the only number with all these properties
— Peyman Milanfar (@docmilanfar) December 31, 2024
Patterns are Beautiful
More here https://t.co/IFkbhqzQq6#math1089 #math #maths #mathematics #algebra #numbers #pattern #happynewyear2025 #HappyNewYear #HappyNewWeek #HappyNewMonth pic.twitter.com/zgdpDkEXd7— Math1089 (@Math1089_9801) December 27, 2024
2025 Pythagorean Triples:
Then have a bit more of that info:
* 2025 is also Pythagorean: 27²+36²=45²=2025.
* Also, when it is 20:25 (does not work in am/pm notation) then exactly 35²=1225 minutes have passed, another square.
* Finally, 20 and 25 are letters T and Y.Bottom line, 2025 will be a good and a polite one.
— Christophe Smet (@christophesmet.bsky.social) December 23, 2024 at 6:13 AM
2025 is the hypotenuse of two Pythagorean triples:
1215-1620-2025, which is (3-4-5) times 405, and
567-1944-2025, which is (7-24-25) times 81.
2025 is a leg in a bunch of Pythagorean triples:
2025-2700-3375, which is (3-4-5) times 675,
2025-4860-5265, which is (5-12-13) times 405,
2025-9000-9225, which is (9-40-41) times 225,
2025-15120-15255, which is (15-112-113) times 135,
1080-2025-2295, which is (8-15-17) times 135,
2025-25272-25353, which is (25-312-313) times 81,
2025-27300-27375, which is (27-364-365) times 75,
1260-2025-2385, which is (28-45-53) times 45,
2025-45540-45585, which is (45-1012-1013) times 45,
2025-8316-8559, which is (75-308-317) times 27,
2025-75924-75951, which is (75-2812-2813) times 27,
2025-82000-82025, which is (81-3280-3281) times 25,
2025-5280-5655, which is (135-352-377) times 15,
2025-136680-136695, which is (135-9112-9113) times 15,
2025-2448-3177, which is (225-272-353) times 9,
2025-227808-227817, which is (225-25312-25313) times 9,
2025-410060-410065, which is (405-82012-82013) times 5
156-2025-2031, which is (52-675-677) times 3,
2025-683436-683439, which is (675-227812-227813) times 3, and finally, this primitive,
2025-2050312-2050313 calculated from 2025, (2025²-1²)/2, (2025²+1²)/2.
Powerful Facts about 2025:
Pour les amoureux des maths :
2025 est le carré de la somme des chiffres de 1 à 9 :
(1+2+3+4+5+6+7+8+9)² = 20252025 est aussi la somme des cubes des chiffres de 1 à 9 :
1³+2³+3³+4³+5³+6³+7³+8³+9³= 2025.C'est le théorème de Nicomaque :
fr.wikipedia.org/wiki/Somme_d...— Pierre Col (@pierrecol.bsky.social) December 23, 2024 at 9:41 AM
2025 is the sum of all the products in the multiplication table from 1 to 9 because:
2025 = (1+2+3+4+5+6+7+8+9)²
This @GeoGebra #MathGIF shows why we also have:
2025= 1³+2³+3³+4³+5³+6³+7³+8³+9³
⏯https://t.co/osAAevIPVe#HappyNewYear2025 pic.twitter.com/KWjLL7vJk5— Vincent Pantal🍩ni (@panlepan) December 31, 2024
Numbers are Beautiful
Number 2025 using only 2https://t.co/C7Ju7UJb7s#math1089 #math #maths #mathematics #algebra #mathtutor #mathstudent #mathtutoring #mathematical #mathteacher #MathsStudent #HappyNewYear #numbers pic.twitter.com/MmXqpLo5Ap— Math1089 (@Math1089_9801) October 21, 2024
2025 Shapes:
2025 is a perfect 45×45 square, but what other shapes can it be in?
Maybe 2025 will be the only square number in your lifetime, but it definitely will be the only centered octagonal number you will live to see.
No es fácil a estas alturas poner alguna #curiosidad sobre el número 2025
Se ha comentado mucho sobre que es un cuadrado perfecto
2025=45² ó incluso más chulo aún:
2025=(20+25)²Pero creo que nadie ha dicho que 2025 es un número octogonal centrado
Feliz año pic.twitter.com/TKfBJZrt5M
— Roberto Santos (@rober_fun) December 29, 2024
Useless facts about 2025:
-it is the sum of the first 9 cubes
-it is the number of spanning trees in K₃,₅
-2²⁰²⁵ is an apocalyptic number, which means its digits contain 666 as a substring
-this circle contains 2025 squares pic.twitter.com/BL5MSRVVXC— Anthony Bonato (@Anthony_Bonato) December 30, 2024
2025 Magic Square:
Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 1 https://t.co/qOdZSEUFyfhttps://t.co/URGYCWBvPn pic.twitter.com/73qMQ2w3Dw
— INDER J. TANEJA (@IJTANEJA) December 31, 2024
Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 2https://t.co/X9imUnmNyh
https://t.co/URGYCWBvPn
Magic Square of Order 4 with 2025. Happy New Year pic.twitter.com/MIH5RTgnrn— INDER J. TANEJA (@IJTANEJA) December 31, 2024
2025 is the sum of consecutive numbers:
2025 es un número educado o cortés (polite number).https://t.co/Q5RTCebrAL pic.twitter.com/nE3wLqHIef
— MATEMATICASCERCANAS (@matescercanas) December 29, 2024
Other Interesting 2025 Sums:
En las siguientes identidades el número 2025 se apoya en otros números y en sus cifras:
2025=1998+1+9+9+8
2025=2016+2+0+1+6
2025=135×1×3×5
2025=632+6^4+3^4+2^4
2025=2030-2-0-3-0— Antonio Roldán (@Connumeros) December 26, 2024
Happy New Year 2025
Pattern starting with 2025
More here https://t.co/IFkbhqzQq6https://t.co/KKQ58mYkxL#math1089 #math #maths #mathematics #algebra #numbers #pattern #happynewyear2025 #HappyNewYear #HappyNewWeek #HappyNewMonth #HappyNewYearInAdvance #happynewmonthchallenge pic.twitter.com/isQvYXcjqu— Math1089 (@Math1089_9801) December 30, 2024
Happy New Year 2025
Single digit representation
More here https://t.co/IFkbhqzQq6https://t.co/qRPeMiOi6P#math1089 #math #maths #mathematics #algebra #numbers #pattern #happynewyear2025 #HappyNewYear #HappyNewWeek #HappyNewMonth #HappyNewYearInAdvance #happynewmonthchallenge pic.twitter.com/3wyKkFLRlU— Math1089 (@Math1089_9801) December 29, 2024