These are great questions for students to be asking as they approach a challenging math question.

At Gathering 4 Gardner, @cardcolm.bsky.social suggested I try the following 3D-printing project. Recall the "napkin ring problem": Take a sphere of radius r and drill out a hole along a diameter so the remaining shape has height h. Then the volume, V = πh³/6, does not depend on R. He thought that

Another 3D-printing suggestion from @cardcolm.bsky.social: Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, it doesn't depend on where the slicing occurs. 1/2

I used to pride myself on writing questions that assessed what we had talked about, but in new & different ways. They'd get plenty of "the standard" questions, but I'd regularly mix in extension problems to see how they can apply their understanding. This was a favorite #mtbos #iteachmath

Small Rhombicosidodecahedron if u even care. I know it can be made with a single (incredibly long) modelling balloon because every vertex only has four lines coming from it, so it has an ✨Eulerian path✨

I wrote a blog post about my G4G16 gift. If you want a copy of your own, download and print the files!

Golly I love living in NYC. I got a ticket for this at noon today. I was filled with childlike wonder for 5 minutes of paper planes swirling down from an oculus… thewangcontemporary.org/events/20000...

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Two knight's tour (32x32 and 64x64). Two terms of an infinite sequence of tours.

Built a “3D” sphere (SVG) to show RYB transformations. Over-iterated in @codepen.io 10% optimization, 90% procrastination. codepen.io/meodai/full/...

A few more experiments! Nothing new but these look nicer than my last set I think! #mathart #mtbos

This afternoon was the "Hands-On Activities" portion of the conference. I brought the supplies (150 laser-cut pieces of wood, 1000 yards of yarn, wood glue, and 50 binder clips) to make a giant cardioid and a giant nephroid. It was fun, and I think they turned out great.

This is a first attempt at categorising @catrionaagg.bsky.social 's puzzles by the techniques used to solve them. My hope is that this makes it easier to use them in class. notes.mathforge.org/notes/publis... #mathsky #UKMathsChat #ITeachMath

We were invited to read from our books, which I did of course. But first I had some opening words, which I thought I'd share with you here. I'll share video too, once that's available.

Charles O Perry sculpture in the lobby of the Hyatt Regency in San Francisco

Vector fields as art. In #MathsToday the students had to create a vector field and overlay it with a picture to create Vector Art. Just a fun little extension at the end of a unit. #iTeachMath

I was gifted a gorgeous origami sculpture of five intersecting tetrahedra. This inspired me to recreate it using Desmos. www.desmos.com/3d/m7hqyu2gpr en.wikipedia.org/wiki/Compoun... @desmos.com #iTeachMath

A tour of tours, an open knight's tour of an 99x99 chessboard. The tour starts in the bottom left corner and ends near the top right corner.

I had a productive day in #Desmos today. I also made a simulation of the refraction and internal reflection that causes rainbows. Enjoy, #EduSky and #MathSky ! #IteachPhysics Full spectrum: www.desmos.com/geometry/hga... (reverse contrast!) Single ray with angles: www.desmos.com/geometry/l32...

Six squares and a quarter circle. The blue square has area 2. What’s the yellow area? #geometrypuzzle

Last two drawing-on-the-cricut experiments -- Hitomezashi patterns! Now I’m done for the day! #mathart #mtbos

And another cool one, using the code provided here! penplotter.art/p/algorithmi... #mathart #mtbos

Finally got an hour to play with Desmos and my cricut. To my eyes, what I was able to make is stunning! 😍 🤩 #mathart #mtbos

Happy (topological) Valentines Day!

Gathering 4 Gardner is this week. I'll be running an activity where we'll make one of these giant cardioids (and a giant nephroid). Today, I'm taking advantage of the sunny, above-freezing day to laser-cut the pieces outside.

One more, which I call "I ❤️ the Cardioid." (A cardioid from one direction and a heart in the other.)

A #genuary sketch that escaped January - Bauhaus Fibonacci www.upstride.ch?id=bauhausfi... #CreativeCoding #CodeArt #genuary2026

Things have been rather busy at the #illustratingMath trimester at the Institut Henri Poincaré for the last two weeks. A number of illustration projects have been started. I'll share some highlights in this thread. (1/6)

#mathstoday started with one of my favorite early probability activities. Students write events on stickies for almost never to almost always and another group tries to sort them. Lots of discussion about wording and googling for more info.

Still playing with these impossible cylinders. Here I have an ellipse with the "Batman curve" in the reflection.

omg everybody go draw a horse this is what the internet was made for gradient.horse

A cool article reddit led me to on how to make some cool math art! penplotter.art/p/algorithmi... #mathart #mtbos

#iteachmath #mtbos What do you call it when you solve a log equation by performing the operation of making, say, 10 the base of each side? log(x+2) = 5 10^log(x+2) = 10^5 What’s the name of this operation?

This question is playing with fire.

This isn't easy to share, but I'm grateful for any support, prayers, or encouragement during this season. Love to all. www.gofundme.com/f/support-fo...

The 2025 Desmos Art Contest gallery is now live 📣! Filter by feature and find your new favorite graph at desmos.com/art 🎨 #mathsky #iteachmath #mathart

Help us bring to life AL, LOGICAL by Xavier Golden and @johngolden.bsky.social, the first graphic novel to be published by Natural Math. I love comics, and Xavier's beautiful panels are adventurous and cool. John's decades of math ed design shine here. Let's go! www.kickstarter.com/projects/nat...

Yay! The kickstarter for our mathy graphic novel AL, Logical is live! www.kickstarter.com/projects/nat... We appreciate any views, retweets, and support for this YA story of curiosity, perseverance, and problem solving.

I have lots of (former) math teacher friends who have been writing curricula. If you're interested in an awesome gig in this space, check out BEAM's current offerings (link: www.beammath.org/work-at-beam) It's a GREAT organization (check it out if BEAM is new to you!) #MTBoS #iteachmath Pleast RT

Finished a post today on chords. It would be really easy to keep going and make a Monte Carlo for random chords, rotations of connected shapes, moire strings, shadow art with strings, etc. www.fractalkitty.com/inquiries-we... #mtbos #mathart #stringart #decemberAdventure #indieweb

A new inquiry activity is posted on Fractal Kitty! www.fractalkitty.com/inquiries-we... This one plays with graphs and can be used as an extension to Sim, Don't Make a Triangle, and other such games. #mtbos #iteachmath #mathplay #accessibleProofs #inquiry #turan #graphTheory #triangles

Project update: Tanya and I have been writing up the results of this project and we've realized that all of the knots in this class of patterns are at most 6 "tangle moves" from each other and at most three tangle moves from what we're calling the "great-great-granny knot" (see alt text).

Here are all 54 distinct knots/links that Tanya and I have identified in our exploration of a specific class of knots on 9-layer Rubik's cubes. We have also determined that this list contains no redundancies & that any of the 4096 patterns that we began with is equivalent to one of these 54 knots.

Day 6 of the math-art class I’m leading. The main activities: lunch and share outs with the math and music class, and setting up an art gallery and pairs of our kids each showing their art pieces and doing an art project with 3 kindergartners. Each pair created their own lesson plan! #mathart #mtbos

Day 5 of the math art class I’m teaching is complete. Today involved finishing up the stained glass window pieces and doing more hitomezashi stitching. #mtbos #mathart

A single-line drawing that is simultaneously an open knight's tour of a 99x99 chessboard and a 3x3 Latin square.

The Interventions We Need • Trigger warning: education consultants read with caution