Playful Math Carnival 183

Welcome to the 183rd edition of the Playful Math Carnival. Begun by Denise Gaskins, previously known as Math Teachers at Play. If you'd be interested in hosting, just drop her a line. Previous editions are listed here! The most recent was Sue Van Hattum's Storytelling Carnival.

183 is a semiprime - though not too mysteriously, as 3 is a factor.

183 squares in this quarter circle. (Cf. A001182) 

New to me was Legendre's Three Square Theorem. Every number can be written as the sum of three squares, unless it is of the form 4^k(8*m+7). (Number theorists are wizards.) 183 = 8*22+7 so it cannot be. Also then, 175 and 191 cannot. Are there any closer integers to 183 which cannot? 

The totient of a counting number is how many natural numbers less than it are relatively prime. The totient of 9 (8, 7, 5, 4, 2, 1) is 6. The totient of 6 (5, 1) is 2. The totient of 2 is 1. Since 9 = 6+2+1, it's the sum of its iterated totients, which makes it a perfect totient number. So is 183! What is its totient sequence? I'll get you started, ϕ(183)=120. 

Projective planes are a fascinating structure that grew out of the study of perspective. One way to generate them is from a finite field. A finite field of order p^n (p a prime) has a projective plane of (p^n)^2+p^n+1 points. The Fano Plane on Z_2 is the most famous example. In our case, 183=13^2+13+1! What's the one before and the one after in this pattern?

183 is also in the sequence n^2-n+1, Hogben's oddly called central polygonal numbers. That means it's on the diagonal of the Ulam spiral. Which side will it be on?

Do you have a favorite 183 fact I've missed?

This edition is dedicated to those regularly producing and sharing new content. 

Regulars

Karen Campe is the definition of regular! Ever month a calendar of problems, and more besides. For example, December 2025 and her Pythagorean Squares activity.

Jim Propp does a monthly deep dive into a different topic each month for his mathematical enchantments column. So carefully crafted and well written. Consider this on Matrix Multiplication. Is it ugly?

Monthly? Pshaw! Pat Bellew has a daily post: on On This Day in Math. But also many other tidbits, like what about monkeys typing Shakespeare? (Of course, some wit pointed out that we already produced a primate who wrote Shakespeare. Shakespeare.)

Denise Gaskins gets close to daily, with her weekly Monday Math Games and Thinking Thursday and other posts besides.

Jenna Laib is a treasure trove. In addition to regular, amazing Slow Reveal Graphs, like this one on butterfly wingspans, she writes deep think pieces like this on culture and identity in math class.

David Petro does a regular feature with lists of resources as well.

Colleen Young does a feature of her own gathering links from all over, but also other posts, like these nifty RISP problems.

Kristin Gray covers a variety of topics, but I particularly enjoyed her list of math stories.

Maths for Humans has a variety of content, but I enjoyed this reflection on learners' problem solving.

Cambridge Mathematics does a monthly Espresso summarizing math ed research, and other features like their new podcast.

The Futility Closet isn't just math, but has amazing tidbits on a frequent basis. Like Lee Sallow's geomagic squares. 

I'm new to Dr. Austin's Maths, but she adds good problems on a regular basis.

Substack

Dylan Kane weekly shares his deep thoughts on math, teaching and teaching math. Here he pitches gradual increase of difficulty, vs release of responsibility.

Fawn Nguyen is back writing again. Some refreshed old hits, some all new content. Always amazing.  Here she's writing about when students write the questions.

Dan Meyer writes a lot about edtech especially AI, but still does some straight teaching talk, too. Like teaching is harder when the math is easier.

Grading for Growth is an alternative grading blog, featuring two of my colleagues among others. Here's Robert Talbert writing about the Four Pillars of Alternative Grading.

Videos

Christina Tondevold's got a regular Buildring Math Minds video series. I thought this one was a big one on the purpose of math learning, Doing and Thinking.

Meet a Mathematician introduces us to mathematicians and math teachers, like the cool Greg Lakey.

Kyle Pearce & Jon Orr have a Make Math Moments video more than once a week, tackling issues like moving towards efficiency.

Watch everything Howie Hua makes. Here he's arguing that 3x8 and 8x3 are different.

Here and There

Grant Snider is a brilliant cartoonist, getting a bit mathy on occasion. Especially with this bit on infinity.

Dan Scher is the leading person I know on Web Sketchpad. Here he shares a new idea Algebra Mazes.

You never know what Tanya Kovanhova is going to write about, but here's a math magic trick.

Sue Van Hattum is writing a terrific math series, getting at big ideas from an accessible angle. She'd love some beta readers... And she has put together a collection of teaching gems from the books.

I've been enjoying the art from the JMM/Bridges 2026 show.

Crazy cool Möbius band explorer from Ben Sparks.

Those fool Teaching Like Ted Lasso guys are back with a new episode on Joy and Softball. 

Sophia (FractalKitty) leads #mathober every year. Lots of interesting bits of math, art and coding were shared. 

Puzzles/Games:

• Karen Campe suggested two. One Up, a kind of number maze.
• Jigsy is the other. That's had an open tab since I first saw it! A geometric puzzle where you can scale the pieces. So clever. I appreciate the levels of difficulty.
• Dive also gets a permanent tab. It's like 2048 for factors.
• A Mathblr user came up with these neat irojirai puzzles on coloring a square.
• I gathered 13 fraction games from a teacher ed course. 
• I also tried to make a tangram like puzzle with 30-60-90 triangles. Here's some examples.

A list of 183 cm tall celebrities? I don't know all these people.

And on that note, I'm out! Hope you found something to get you playing with math.