@phonner@mathstodon.xyz
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phonner

@phonner@mathstodon.xyz

Math teacher, instructional coach, author (Painless Statistics), columnist (Quanta Magazine).

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phonner, to random
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Any graph theorists willing to help me out? I'm trying to better understand triangle-free graphs and maximal independent sets, and something doesn't make sense to me. The wikipedia entry for triangle-free graphs says that in an (n)-vertex triangle-free graph, an independent set of size (\sqrt{n}) is "easy to find": Either one vertex has more than (\sqrt{n}) neighbors, which I get as this forms an independent set. But then it says that if every vertex has less than (\sqrt{n}) neighbors, then "any maximally independent set must have at least (\sqrt{n}) vertices". This I don't get, and it seems obviously false for the pentagonal loop. Am I missing something?

https://en.wikipedia.org/wiki/Triangle-free_graph#Independence_number_and_Ramsey_theory

phonner, to math
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Started our trigonometry unit yesterday and shared one of my favorite articles from Evelyn Lamb: Ten Secret Trig Functions Your Math Teachers Never Taught You.

I'm thinking about putting a haversine identity on the next test.

https://blogs.scientificamerican.com/roots-of-unity/10-secret-trig-functions-your-math-teachers-never-taught-you/

clive, to random
@clive@saturation.social avatar

“I had a guy come in with his family ... and he did 16 rounds of shrimp scampi. He was there for over two hours on a busy Friday night. They had one of my biggest tables. I just had to watch this man eat plates upon plates of the scampi, which isn’t even served over pasta. It’s shrimp in a garlic-wine butter.

"It was so gross.”

Red Lobster employees tell grim tales of the chain benighted "endless shrimp" deal: https://slate.com/life/2024/05/red-lobster-restaurant-closing-bankrupt-endless-shrimp.html

phonner,
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@clive

phonner, to math
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Nice write-up from Ole Peters about ergodicity and the "infamous" coin toss. I've been sharing these basic ideas in my math classes for the past few years, and I think it really introduces students to new and important ways of thinking.

#math #statistics #economics #probability #MathEd

phonner, to math
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Inspired by my brilliant student (https://mathstodon.xyz/deck/@phonner/112419322877058443) I've been playing around with (e)-like sums. Here's a fascinating one!

[ \sum_{n=0}^{\infty} {\frac{n^4}{n!}}=15e ]
This is strange enough to provoke wonder, but simple enough to serve as an entry-point to an interesting generalization.

#Math #Calculus

phonner, to math
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I gave my geometry students some ChatGPT-generated "proofs" this week to review. There were several examples, each designed to illustrate a different point. One was a "proof" that the diagonals of a rectangle are congruent, which contained several errors. I was proud that several students immediately identified how dangerous it was: "It sounds like it is correct, until you look more closely at it."

phonner, to math
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Student 1: That's the craziest shape I've ever seen!
Student 2: That's a hyperbola.
Student 1: And that was hyperbole.

Believe it or not, a true story!

phonner, to random
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I really don't understand why people who left Twitter angry and disillusioned would use Bluesky. It's vulnerable to the same problems. It was started by the exact same person!

phonner, to random
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Logged into Twitter to look around, as I occasionally do. I was met with:

• Humblebrag moralizing from people who don't understand the morals they are bragging about possessing
• Several posts intentionally designed to elicit a negative reaction from me
• A few thoughtful posts with no engagement whatsoever
• Four people complaining about Twitter and/or social media
• Two people I miss hearing from

phonner, to random
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There are very few circumstances under which I would choose to eat a raisin.

phonner, to random
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One of my summer projects was to build a Mastodon bot, and I did it! The bot doesn't do anything that hasn't been done before (it generates a random Wikipedia page, pulls the title and link, and posts it), but it's something I haven't done before. Many thanks to Terence Eden's (@Edent) easy-to-follow guide (here: https://shkspr.mobi/blog/2018/08/easy-guide-to-building-mastodon-bots/)!

https://botsin.space/@RandomWikiBot

phonner, to math
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I was not expecting to read about a polygamous mathematician obsessed with the fourth dimension in this brief history of the "jungle gym"!

https://www.npr.org/2023/11/08/1209932614/jungle-gym-playground-monkey-bars-maths-hinton-fourth-dimension

phonner, to math
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This isn't the first time I've found an online cross product calculator to be unreliable.

#Math

https://www.symbolab.com/solver/vector-cross-product-calculator/%5Cbegin%7Bpmatrix%7D1%260%260%5Cend%7Bpmatrix%7D%5Ctimes%20%5Cleft(%5Cbegin%7Bpmatrix%7D1%260%260%5Cend%7Bpmatrix%7D%5Ctimes%5Cbegin%7Bpmatrix%7D0%261%260%5Cend%7Bpmatrix%7D%5Cright)?or=input

phonner, to ukteachers
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Sweden has declared a "system failure" regarding its "free schools", which are publicly funded but privately run for profit. I wonder if the same will be said about charter schools here in the US in 30 years, after maximum profit has been extracted from the practice.

https://www.theguardian.com/world/2023/nov/10/swedens-schools-minister-declares-free-school-system-failure

#Education

phonner, to random
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A Bribe for a Five-Star Review, by Tanya Khovanova
https://blog.tanyakhovanova.com/2023/07/a-bribe-for-a-5-star-review/
I bet this happens often! Sad, but not surprising, that Amazon seems to protect this kind of behavior.

phonner, to math
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My latest column for @QuantaMagazine is about one of my favorite mathematical ideas: transitivity! Well, technically it's about intransitivity. Also, inspired by the football playoffs!

https://www.quantamagazine.org/the-surprisingly-simple-math-behind-puzzling-matchups-20240125/

phonner, to math
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Student: "The distance to the far end of the circle is three."
Me, skeptically: "Where is the 'far end' of the circle?"
Student, gesturing: "On the far left side."
Me, intentionally choosing a point on the left that is close to, but clearly not, the farthest left: "Oh, you mean here?"
Student pauses: "I understand what you are trying to do. But I don't know how to be clearer."
Me, surprised: "What am I trying to do?"
Student: "You are trying to force me to be more precise in my statements."

Pretty impressed at how this student has me entirely figured out after four days.

#Math #MathEd

phonner, to random
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I righted a lifetime wrong this weekend by finally learning to whistle with my fingers.

phonner, to ukteachers
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Texas will use AI to grade free response questions on standardized exams for reading, writing, science, and social studies this year.

"For $50, students and their parents can request a rescore if they think the computer .. got it wrong."

https://www.texastribune.org/2024/04/09/staar-artificial-intelligence-computer-grading-texas/

phonner, to science
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Guess the theorem.
#math #stats

Distances from a set of points in the plane to a pair of rotating axes.

phonner, to math
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Another year, another few students suggesting a brilliant approach to computing ( \int\sqrt{1-x^2} dx)!

https://mrhonner.com/archives/20967

#Math #Calculus

phonner, to math
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Brian Conrad, the Stanford mathematician who has written extensively about the problems with the proposed California Mathematics Framework (CMF), is now the subject of a formal complaint filed with Stanford University by the President of the central section of the California Math Council accusing him of "reckless disregard for academic integrity".

https://sites.google.com/view/publiccommentsonthecmf/#h.u9k2csw8r9s4

phonner, to random
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Anyone else seeing some strange behavior on Mathstodon today? I've got old posts popping up to the top of my feed and I'm not seeing replies in my notifications tab.

phonner, to random
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I was recently subject to local TV news for the first time in a while. Still the same. Pretty much every story is BE AFRAID BE VERY AFRAID! with some occasional human interest thrown in to break up the monotony.

phonner, to random
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You might think that teachers who complain that their students can't do X might eventually realize that since it's their job to teach their students to do X they are actually complaining about themselves. But you would be wrong.

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