Patrick Honner

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

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Last Notes

2026-02-06 02:18:21 GMT

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@nprofile…gu9p It gets better. The next chapter's principle is "Give honest and sincere appreciation", which I am in 100% agreement with. It's a fun and easy read, and it definitely says something about its time as well.

2026-02-06 00:28:17 GMT

I'm currently reading "How to Win Friends and Influence People". As an example of his first principle — "Never criticize, condemn, or complain" — Dale Carnegie writes about a test pilot who is forced to make an emergency landing because the technician put the wrong fuel into the plane. Carnegie lauds the pilot's response: Instead of criticizing the technician, he tells him that he wants him to service his plane tomorrow, because he knows he won't make that mistake again. Because it's more important for this technician *not to be criticized* than it is for the pilot to *not die in a plane crash*? 30,000,000 copies of this book have been sold?

2026-01-08 22:20:44 GMT

I've always found it cool that if you double the smaller acute angle in a 3-4-5 triangle you get the larger acute angle in a 7-24-25 right triangle. You can see this as a consequence of the double angle for sine. If \( \alpha \) is the smaller acute angle in a 3-4-5 triangle, then
\[ \sin (2\alpha) = 2\sin\alpha\cos\alpha=2\frac{3}{5}\frac{4}{5}=\frac{24}{25}\]
In fact, if the sine and cosine of an angle are both rational, then so will be the sine and cosine of twice that angle. This gives a way to turn Pythagorean triples into new Pythaogorean triples!
For example, suppose \( \alpha \) is an acute angle in a right triangle with \(a^2 + b^2 = c^2 \). Then
\[ \sin 2\alpha = \frac{2ab}{c^2} \]
\[ \cos 2 \alpha = \frac{a^2-b^2}{c^2} \]
By the Pythagorean identity
\[ \left(\frac{2ab}{c^2} \right)^2 + \left(\frac{a^2-b^2}{c^2} \right)^2 = 1\]
And so
\[ \left(2ab \right)^2 + \left(a^2-b^2 \right)^2 = \left(c^2\right)^2\]
which of course also follows directly from algebra.
For example, using this process
\[ (3,4,5) \mapsto (7,24,25) \mapsto(336,527,625)\]
#Math #MathEd #Mathematics #NumberTheory #Algebra #Geometry

2026-01-04 13:15:48 GMT

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@nprofile…vhdw I think the role the origin / zero-vector plays also contributes to non-obviousness for me. The geometric act of reflection *itself* isn't linear, it's a specific kind of reflection (through something that passes through 0) that is linear. Same with translation -- at first glance, whatever geometric intuition suggests that reflection is linear would probably also apply to translation in my mind, which of course it isn't.

2026-01-04 02:13:43 GMT

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@nprofile…vhdw We work from the geometric construction of reflection, and it takes some work just to establish what \[ f (c\vec{u})=cf(\vec{u}) \] and \[f(\vec{u}+\vec{v})=f(\vec{u})+f(\vec{v})\] mean. Then showing they are true requires some work! It's not hard, but it's not trivial!

2026-01-04 01:16:57 GMT

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@nprofile…vhdw I take (what I think is) an unusual approach in my Linear Algebra class by proving that reflection *is* a linear transformation, which I don't think is at all obvious!

2025-11-30 15:37:35 GMT

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@nprofile…8eua He sounds like an LLM!

2025-10-04 15:54:26 GMT

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Steven Strogatz shared with me a wonderful collection of open problems in the packing of squares within squares that I included in the piece. Some of the diagrams are crazy! Here's the best known packing of 272 unit squares in a square with side length less than 17.
#Math #MathEd #Geometry
https://media.mathstodon.xyz/media_attachments/files/115/316/687/055/710/712/original/056f4273ffab60c1.png

2025-10-01 00:22:41 GMT

My latest piece for the New York Times Learning Network is out, and this one is all about mathematical packing!
https://www.nytimes.com/2025/09/30/learning/lesson-plans/unpack-the-math-of-packing-with-steven-strogatz-and-the-new-york-times.html
#math #MathEd

2025-05-24 14:04:14 GMT

Am I the only one who feels like Google Drive is so poorly designed and unintuitive that it borders on being unusable?

2025-03-11 21:33:13 GMT

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@nprofile…749s She did! She said she watched your videos and read your paper. I was impressed. I had no chance of getting it!

2025-03-11 20:56:34 GMT

@nprofile…749s Sorry if a student of mine pestered you! I gave her a puzzle you designed (that I acquired years ago) and told her to figure it out. I didn't expect her to email you asking for help!

2025-03-02 17:47:20 GMT

One of my beliefs as a high school #math teacher is that every course is a geometry course, which I guess is the opposite of what another teacher once told me: "Geometry is a crutch".
#Math #MathEd #Education

2025-01-31 11:58:14 GMT

Excited for the upcoming book "The Proof is in the Code", by Kevin Hartnett. This "definitive account of the birth and rise of Lean" will be the first book from @nprofile…zu62's Quantabooks!
https://www.quantabooks.org/
#Math #SciComm

2024-09-04 21:28:49 GMT

Math teachers often feel superior because their tests are more "objective" than those in other subjects. Who writes the questions? Who decides what concepts get tested? Who decides how partial credit is assigned? Who decides how the results are interpreted? It's all subjective, all the way down.
#MathEd #Teaching #Education

2024-09-02 14:34:34 GMT

70 MB for a metronome app? Is that what the world has come to?

2024-09-01 23:11:19 GMT

This graph guessing game is pretty interesting! You're shown a graph, and you have to guess (from five options) what is being displayed. A good tool for statistical literacy in math and statistics classrooms!
https://www.graphs.world/
#Math #MathEd #Statistics

2024-08-11 22:19:11 GMT

Math teacher Gary Rubinstein gives five reasons why the Illustrative Math curriculum mandate in NYC is destined to flop.
https://garyrubinstein.wordpress.com/2024/08/09/illustrative-math-the-new-curriculum-that-nearly-every-algebra-teacher-in-nyc-has-to-start-using-this-fall-and-why-it-is-destined-to-flop/
#Math #MathEd #Teaching #Education

2024-07-25 17:50:23 GMT

More impressive results from the automated theorem prover / proof assistant / formalization community. Things are happening fast!
#Math #MathEd #MathTeaching
https://www.nytimes.com/2024/07/25/science/ai-math-alphaproof-deepmind.html?unlocked_article_code=1.900.yOkt.837ojvZKANn7&smid=url-share

2024-06-25 03:10:24 GMT

Sorry to see Edmonton lose, but I enjoyed getting caught up in the Stanley Cup this year! They made a great run at the end.
#NHL #Oilers #StanleyCup #Edmonton

2023-08-04 14:29:25 GMT

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 (@npub19lt…qfjk) easy-to-follow guide (here: https://shkspr.mobi/blog/2018/08/easy-guide-to-building-mastodon-bots/)!
https://botsin.space/@RandomWikiBot

2022-12-08 11:50:45 GMT

My early morning math realization is that instead of thinking of a rotation matrix as
\[ \left[ \begin{array}{cc}cos \theta & -sin \theta \\ sin \theta & cos \theta \end{array} \right] \]
it makes more sense to think of it as
\[ \left[ \begin{array}{cc}cos \theta & cos (\theta + \frac{\pi}{2}) \\ sin \theta & sin(\theta + \frac{\pi}{2}) \end{array} \right] \]
as this makes it obvious that the transformation preserves orientation and the angle between the standard basis vectors.
#math