Matt Enlow

YoU gEt SuMmErS oFf

The only piece I'm a little iffy on is "so every vertex has degree 3." How does that follow?

Wait... a vertex can't have degree 2... and the sum of the degrees is twice the number of edges...

Never mind, I got it! 😁

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

(Is it possible to prove it without first finding the individual values of a and b?)

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

Interestingly, I have students who would agree that the sets of even and odd _natural numbers_ are the same size, but quibble over whether the even and odd _integers_ are the same size (see the second image).

The one-to-one correspondence idea kind of arose naturally when we were comparing ℂ to ℝ².

Right. I feel like there exist concrete examples of the proper-subset model that are either explicitly self-contradictory or just don't "feel right." I'll have to think about it.

I’d rather not introduce a new object (“infinite string”). I’m thinking about temporarily limiting the scope to infinite subsets of N. How do they compare?

After each class I tried to summarize the conversation on a Page in Canvas. Here's where we currently stand. Now I have to think about how best to proceed—and I want to do so WITHOUT any investment in them landing at the "traditional" answers! Which will be tough.

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.

Okay I feel better now having made this

a man says why are you punishing me ALT: a man says why are you punishing me

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
🟨🟨🟨🟨
🟦🟦🟦🟦
🟩🟩🟩🟩
🟪🟪🟪🟪

a close up of a man 's face with the word interesting written below him ALT: a close up of a man 's face with the word interesting written below him

Oh, and another student insisted that there ought to be different "degrees of infinity" to distinguish between, say, ℤ and 𝒫(ℝ²), because the latter is just clearly so much bigger than the former, even though they're both infinite.

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 😑

In fact, any black-and-white image on the plane can be thought of as a subset of R^2, where the black points belong to the subset and the white points do not. So the text “INFINITE” in Figure 1.4(c) is a subset of R^2 and therefore an element of P(R^2). By that token, P(R^2) contains a copy of the page you are reading now. Thus, in addition to containing every imaginable function and every imaginable black-and-white image, P(R^2) also contains the full text of every book that was ever written, those that are yet to be written and those that will never be written. Inside of P(R^2) is a detailed biography of your life, from beginning to end, as well as the biographies of all of your unborn descendants. It is startling that the five symbols used to write P(R^2) can express such an incomprehensibly large set. Homework: Think about P(P(R^2)).

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

For the curious, adding "style="vertical-align: top;"" to the <img> tag that Canvas generates seems to have gotten close enough to what I want. 🤷‍♂️