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

Yep! Thanks to @joeldavidhamkins.bsky.social www.infinitelymore.xyz/p/monkey-mad...

Given our ability to program clouds of drones, it can't be too long before we get self-rearranging desks in our classrooms Pre-program a few arrangements, then just push a button and wait 60 seconds, and boom

Fibonacci Voronoi-ing in #MeshLab (with assistance from #Mathematica, of course)

For today’s Advanced Topics test I wrote my own @joeldavidhamkins.bsky.social -style question 😁 #iteachmath #MathSky

"I’m honored, obviously, to get to be one of the people that gets to choose which movies get made, and which ones don’t. That’s huge. And I got into all this because I love movies! But… now I have this fear… that my job is to ruin them." -- Matt Remick (Seth Rogen), "The Studio" Man do I feel that.

I got tired of my Alg II Honors students asking me when their tests would be graded, so I created a Google Sheet that simulates a "Progress Bar." And I don't have to update it manually; I tied it to a separate Sheet where I log their scores on individual questions, so it updates as I fill it out 🤓

Get you a Department Head who recognizes when a meeting can be an email and cancels the former accordingly 🥰

My second OEIS sequence has been approved! oeis.org/A390274

Y'all, I made an example problem in Geometry class this morning that had a 67° angle in it, and the most I got was smirks. I think we're finally on the other side of it.

TFW you search for an answer to a very niche technical question and your primary result is someone else asking the same question on some message board, ten years ago, with zero responses

The latest iteration of this Fibonacci spiral #mathgif uses closed BSplineCurves instead of polygons. There is this odd behavior I'm observing away from the center that reminds me of soap bubbles combining. I can't decide how I feel about it. #Mathematica #mathart

A Voronoi variation on Saturday's #mathgif #mathart #Mathematica

“It took me four years to paint like Raphael, but a lifetime to paint like a child.” — Pablo Picasso I've seen this quote before, but it's hitting me particularly hard today. There's something here relevant to math education (and I bet @mathgarden.bsky.social has already written about it 😉).

Just a little coding diversion before doing some schoolwork #mathart #Mathematica

After getting the mail, my wife calls to me from another room, “Your Victoria’s Secret catalog came.” “Huh?!?” Baffled, I go and find her. At which point she hands me the L. L. Bean Holiday Catalog. It’s good to be gotten.

Not today, Satan

Every time I reflexively hit ⌘S to save my work in a Google Doc or Google Sheet, I picture the Google gods somewhere chuckling to themselves and enjoying my preciousness

I have a conjecture!

*starts writing a Trimester-I comment for an Advanced Topics student* *talks about the great work this student did on an open problem* *starts wondering things about the problem* *sparks up #Mathematica* *an hour passes with no writing taking place* 😑😑😑 #iTeachMath #ADHD #MathSky

The older I get, the less interested I am in contrived "contest problems," and the more interested I am in - focusing on deep, enduring truths - dwelling in mystery, contradiction, enigma - finding beauty in simplicity #Math #MathSky #iTeachMath

If g(x) = 4⌊x⌋-2x, write a definition for g⁻¹(x). (⌊x⌋ is the "floor" or "greatest-integer" function.) #iTeachMath #MathSky

Not particularly difficult, just... makes you think. #iTeachMath #MathSky

I think I've put my finger on something that really bothers me about CPM Geometry. The questions they ask SOUND like they are soliciting student ideas ("What do you think..."), but they are expecting a very specific answer. DON'T SOLICIT STUDENT IDEAS IF YOU'RE NOT GOING TO VALUE THEM. #iTeachMath

One-to-one functions in Alg II Honors today. That means it's time to share one of my favorite little aphorisms: If a function's one-to-one, Then what it does can be undone. #iTeachMath #MathSky

If one wanted to, one could probably write a question about pursuit curves set in the "Weapons" universe

If you see this and think “augmented Tricsuit,” #YouMightBeAMathematician

It's worth a little more detail: Her teacher had them write a proof, then the next question said something like, "If you used more than 4 steps in the previous proof, could you write a proof using fewer steps than you did?" 😒 [1/4]

After receiving little more than groans and eye rolls when helping my 14yo daughter with her math homework over the years, I finally got it last night after talking her through a Geometry proof: "Why couldn't YOU be my math teacher?"

On of my geometry students just talked about the Angle Addition Prostitute and I think my day is over.

I'm just trying to write an email to my wife outlining our schedule for the next couple of weeks. It looks like I've got at least three different "checkers" telling me I'm doing it wrong. 😑

I asked ChatGPT a True/False question from Hammack's "Book of Proof," and it did something I hadn't seen it do before. It first said the statement was true, and then as it explained its "reasoning," it wound up convincing itself that the statement was false (which it is). #MathSky #iTeachMath

A certain polyhedron has 6 faces and 8 vertices. Must it have a hexagonal cross-section? #iTeachMath #math #WonderWithMe

Oooh, new mathematical quackery just dropped

Once every couple of weeks we get an email with the subject "PD Newsletter" making us aware of various PD opportunities available to us. But when I see it appear in my inbox, my first thought (if you could even call it that) is to respond, "PD Newsletter? What the f___ does THAT mean?" #iykyk

Consider a regular heptagon with side length 1 unit. Its diagonals have two distinct lengths. Prove that the sum of those two distinct lengths is equal to their product. #iTeachMath #MathSky

My Advanced Topics students are super into this whole "degrees of infinity" thing. They've spent most of two whole class periods wondering and brainstorming. I spent that time trying not to let my knowledge of "the answer" seep out too much in my attempts to help them prime their thinking.

My 14yo daughter asked me to check her work on a Geometry worksheet. It was some of the most boring and soulless drudgery I've seen. The "We sprinkled some random algebra into repetitive questions about the Angle Addition Postulate and the Segment Addition Postulate. Boom. Geometry" type.

TIL that the phrase "good doobie" came from Romper Room 😮

Beginner's luck? Connections Puzzle #837 🟨🟨🟨🟨 🟦🟦🟦🟦 🟩🟩🟩🟩 🟪🟪🟪🟪

Introduced Advanced Topics to 𝒫(ℝ²) today. Minds were appropriately blown. Including my own, when one student referred to the humans in the room as "elements of 𝒫(ℝ³)."

A student drew this portrait of me on her test today

Reminds me of the time my dad texted me "Just got shot" to let me know he'd just gotten his COVID shot 😑

Can't wait to get to this bit of Hammack's "Book of Proof" with Advanced Topics 🤯🤯🤯 #iTeachMath

Join me

Pretty wild that two-hit wonder The Escape Club’s two hits were “Wild Wild West” and “I’ll Be There.” Just… two completely different songs.

A colleague asked if she could decorate a room we both teach in. I said “Sure.” She made it clear I could veto anything she put up, but I was all, “Nah, whatever’s fine.” Until…

One minute I was prepping for classes. The next minute I found myself on the webpage of a Vermont falconer. I'm sure there was a linear path I followed to get from the former to the latter, but I'll be darned if I could tell you what it was. #ADHD

If you’re an authoritarian when your party’s in power and a libertarian when they’re not, I regret to inform you that you are merely an authoritarian