Test new black paper and new colored pencils ... by constructing a hyperboloid ... by letting a line segment rotate about an axis! Also: Adding proper annotations of points and lines for the first time. #MathArt #SciArt

Here are a few more curved origami pieces I made. Technically, I made them so the crease lies in the same plane. But if I make the strips narrow enough relative to the object's size, you can get the over-and-under behavior to work pretty well. I could have made all of these except the 5₁ knot

I like the proof using complex numbers, which is how Van Aubel himself proved it (using the strange notation where √ as a stand-alone symbol means what we call i). You might enjoy my video on the subject. youtu.be/pUSI91Mo7LU

On our last precalc class, we went outside and did some sidewalk math! #mtbos

Does understanding the Math Practices seem impossible? I think so and I rewrote them in an attempt to make them readable. In this blog post I share my revised version of MP 4 as well as a link to download all 8 MPs in English or Spanish as a printable PDF. robertkaplinsky.com/making-...

Students were out of their seats collecting data for a related rates lab today! They compared experimental data to theoretical solutions for the classic sliding ladder, the inflating balloon, and more. A fun day of "math in motion." #ITeachMath #Calculus pbbmath.weebly.com/blog/hands-o...

New art for the art wall outside my office #mathart

A deltahedron I made at #100factorial today with the polydron triangles. It’s a size-three octahedron with three size-one tetrahedra on each face. The whole shape has 120 faces, 180 edges and 62 vertices, with exactly 40% of the edges concave. It took me two hours to make, and some extra hands.

what a final @todos-math.bsky.social e-news message! congrats to @dingleteach.blacksky.app for her leadership of TOODS as she segues into Past President; congrats to @karikokka.bsky.social as incoming President; and congrats to two incoming Directors, including Dr. Sara Rezvi! 🔗 www.todos-math.org

Algebra teachers, check out these three rational exponent problems from Bryan Anderson. See the hints and answers on Open Middle: www.openmiddle.com/rational... www.openmiddle.com/rational... www.openmiddle.com/rational...

In #mathstoday (well, actually yesterday) my Year 12s tackled another great Underground Maths problem. This one worked really well & stimulated loads of discussion, helping cement their understanding of logs. Definitely recommend 👍🏼 undergroundmathematics.org/exp-and-log/...

Any chance any of you math folks out there want to uplift one of my students? She created an instagram with a fictionalized journal of mathematician Srinivasa Ramanujan [ www.instagram.com/lucie.r.vk_e.... Personally her journal floored me! *I'd love for her to get some followers!!!*

I have a high school student who created a fictitious journal for Ramanujan for a class project, after researching his life. It's so cool, and has entries from a fictitious Ramanujan along with others. If this intrigues you, please follow&share this insta: www.instagram.com/lucie.r.vk_e... #MTBoS

A problem to start calculus class on Monday. We're not to integration yet, but I want to start nudging student thinking in that direction. Plus a bit of retrieval practice and creative thinking/problem solving. #ITeachMath

working with students on problems of the nature: How many ways can you distribute 10 cookies among 3 people if the max # per person is m? For e.g. m = 4, you can ignore m and make the full list of all distributions. Then naively cross off every entry each time it contains an entry ≥ 5. But, then+

This is so cool! Given only the "exponential minus log" function, elm(x,y)=exp(x)-ln(y), and the constant 1, you can perform +, -, x, ÷, exp, ln, trig, powers, roots, etc. You can also obtain e and π! See arxiv.org/pdf/2603.21852 and arxiv.org/src/2603.218...

I've confirmed to speak at the NCTM Annual in Denver 🗣️🎤 Here is the abstract: 🪑: www.aievolution.com/ntm2601/Abst... Deets: #NCTMDEN26 Annual Meeting, October 28-31 in Denver! www.nctm.org/denver2026/ See you there??? #iTeachMath ♾️ #MathSky 🧮

I had a student who essentially needed something to yield 0 when positive and to yield 1 (or -1) when negative. They came up with this idea 💡 which was oh so lovely. #mtbos I love creativity and out of the box thinking.

Every day in Calculus, there's a warm-up on the board as students walk in. Gets them thinking and sets the tone before we even start. A few from this week: Crack the Code, Which One Doesn't Belong?, and four trig derivatives. Low stakes, high engagement. #ITeachMath #MathsToday

I probably won’t be able to read this book (Proof: How the World Became Geometrical) for a while. But I thought the two other books by the author were great. And what a lovely cover! #mtbos

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.)