In each diagram, the green area and blue area are equal

My feelings about A.I. and math

If just one other person gets this reference I'll be thrilled #GreatAmericanStateFair

Suppose a hollow cone with radius 15cm and height 20cm is being filled with water. If it were base-down, the area of the surface of the water would decrease as the cone filled; if, instead, it were balancing on its point, the area of the surface of the water would increase as the cone filled. [1/2]

Just found this. It will take everything I have to give the "Ditch Geometry" proponents a fair hearing. I'm going to need some time before even pressing Play, though, to feel my initial feelings of sadness and anger that this is even something we're contemplating. www.youtube.com/watch?v=8RE1...

The integers from 1 to 18 can be arranged in a circle so that, when following the circle (counter-clockwise in the below example), every number is the sum of the previous two (mod 19). For what other mods can we do this? That is, for what other integers m can the integers 1 to m-1 be so arranged?

Currently wondering: Can an equilateral pentagon have five distinct interior angle measures that are all rational multiples of π radians? If we remove "distinct," there's at least the regular pentagon with five angles of 3π/5, and another pentagon with two π/2's, two 5π/6's, and a π/3. #MathSky

A couple of Advanced Topics students reviewing for their test today #iTeachMath

Another fun arithmetic sum challenge #iTeachMath #iTeachMaths #MathSky #MathsSky

I always roll my eyes when an A.I. chatbot describes something as "fun," or reports being "curious" about something. Because... no. That's not what's happening. This was a new one on me, though. Why not just omit the "us"?

I am still-occasionally-reflexively-hits-Command-S-even-when-working-in-Google-Docs years old

🎶 … by the moon and the stars in the sky… 🎵

Text from the wife

A parabola rolls along a flat surface. What path does its focus (the red point) trace? Another parabola? Or something else? #iTeachMath #math #maths #mathgif #mathgifs #mathsgif #mathsgifs

Today in Advanced Topics we tried to create a "quadratic formula" for solving quadratic equations in ℤₙ. I'd never done that before. Wasn't planning on doing it today. But that's where our rabbit hole led us. We haven't worked out all the kinks, but the messiness is part of the fun. (Ask any kid.)

An xy projection of the 3D Halverson attractor. I coded it in #Mathematica, then asked #ChatGPT to port it to html/js so it can run in a browser. That's what you're seeing here.

Springtime in Algebra II Honors is fun-arithmetic-sequence-problems season... #iTeachMath #iTeachMaths #math #maths

Four unit spheres, centered at (±1,±1,0)... and their convex hull. Each in a single line in #Desmos 3D. Can you do it? #iTeachMath #math #maths #geometry desmos.com/3d

> image of Jesus eating a hotdog, the text underneath it reading “He Is Glizzin’”

What fresh hell is this

My 15yo son manages to get pizza sauce on every new article of clothing the first time he wears it. Even if we haven't eaten pizza. Somehow he still makes it happen.

Going to try to discover some log rules in Alg II Honors today #iTeachMath

My kids introduced me to this and I will never forgive them for it

Kitchen hack: Use a poker chip set—heavy, but low center of gravity—to press tofu

A "making of" my #mathart post from yesterday

🙄

Just checking in on my Janus account. This is what I see (minus personal specifics): the Contrarian fund living up to its name

One minute you're puzzling over a simple probability question, the next minute you're unironically typing out an expression that looks like this

Hyperbolic surfaces spotted at the Andrew Gn exhibit at the Peabody Essex Museum

Okay this one is a beast #math #mathchat #maths #mathschat #probability #iTeachMath #MathSky

Here's a fun Geometry quickie: A particular polygon has only two distinct interior angle measures: 165° and 166°. How many sides does it have? #iTeachMath

Me figuring out how to make Canvas API calls from Google Sheets

I vibe-coded a web app that allows you to walk around on the surface of a gyroid. It's just as disorienting as you'd expect. velvety-arithmetic-0a8353.netlify.app

It's kind of a running gag in our house about how boring my Facebook posts were before we had kids, but this one kind of takes the cake

MAA MathFest is in Boston this year! I've never been, and always wanted to. A significantly reduced registration rate for K-12 teachers? And I might be able to bring one of my kids as a "guest"? This may be my opportunity! Anyone else I know planning on attending? maa.org/event/mathfe...

Three words/phrases you never want to hear from your plumber when you're describing your problem over the phone: "absolute nightmare," "worst-case scenario," and "jackhammer"

One superpower #math gives me is the ability to picture an interesting object in my head, spark up #Mathematica, and within a few minutes figure out how to make it "real." It's intoxicating! (code in ALT)

Just arrived 😍😍😍

After a few weeks of repeated discussion and revision, here is where the Axiom (& Theorem) List for ℤ that my Advanced Topics class has been generating from scratch—with some prodding and guardrails provided by me—currently stands. (Proofs of the Theorems are located elsewhere.) #MathSky #iTeachMath

Why are the emails that require the meagerest of replies—"All set!" "Thank you!" "Great! See you then!"—sometimes the hardest to get myself to write?!? Makes no sense. Stupid #ADHD brain...

Student 1: I don’t get this. Student 2: Oh! Let me show you a trick my tutor showed me. Me: 😑🤐 S1: *shows S2* S2: OMG, that is so EASY! Mr. Enlow, why didn’t you teach us this?!? Me: 😑😑😑😑😑

Please stop teaching the "X method" for factoring. And please de-stigmatize "guess-check-revise." Yes, it's slower. But it yields SO much more actual learning and understanding than blindly following an algorithm does. #iTeachMath #MathSky

🤔🤔🤔

An update to my ring project. This was not easy to achieve! #mathart #3DPrinting #Mathematica #MeshLab

Now that Shapeways has apparently risen from its ashes (with the help of @thangs3d.bsky.social ), I'm trying to design an interesting ring. Copies of this one nestle inside each other nicely. #3DPrinting #Mathematica #MeshLab

Finally got around to this. I’ve only read the Introduction so far, but it is so good. I want to force everyone in the world to read it (and decide for themselves whether to continue). I’ll have to settle for “everyone in my household.” 😁 @jsellenberg.bsky.social

Cool! The circles in an Apollonian Gasket can all have an equation of the form (n|x|-a)² + (n|y|-b)² = 1, where n is a positive integer, and a & b are non-negative integers < n. www.desmos.com/calculator/6... #MathSky #iTeachMath

Three mutually tangent spheres with radii 1, 2, and 3 units are centered, respectively, at (0,0,0), (3,0,0), and (0,4,0). There are only two planes tangent to all three spheres, and they intersect in a line in the x-y plane. Find an equation (in x&y) for that line. #MathSky #iTeachMath #math #maths

Last day of classes. Second-to-last class of the day. Algebra II Honors. A student says, "Why did I bother coming to school today? All I've done, in multiple classes, is watch 'Elf'!" 🤨 (Said student was somehow NOT happy that we were "actually doing math" today. 🤷‍♂️) #iTeachMath