@benjamin_leis

Systems programmer, parent, volunteer Math Circle leader and general math enthusiast. Team puzzles and #geometry @benleis@mathstodon.xyz

 Seattle, WA
blog.mathoffthegrid.com
Joined January 2015
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  • Following214
  • Followers579
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It's that time again: Collected Problems 5 is done: bit.ly/2nTb9su Collected Problems 6 is starting: bit.ly/3d8vL6k
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It's mostly codifying my current behavior but I'm done here.
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For @DavidKButlerUoA - spoilers in the reply
David Butler@DavidKButlerUoA15 Sep 2023
Replying to @DavidKButlerUoA
(1-x)²=x³(1-1/4 x) 1-2x+x²=x³-1/4 x⁴ 1/4 x⁴-x³+x²-2x+1=0 x⁴-4x³+4x²-8x+4=0 Not feeling good about that at all!
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more replies
If you suspect that the whole triangle is a 45-45-90 (which does turn out to be true) that also gives some test Polynomials you can divide out and see if there is a remainder.
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But my original remark was whether this could be avoided without assuming similarity of the triangles so carry on
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Apropos of nothing in particular: My model of learning is that more knowledge/instruction can never hurt and usually helps. I need solid evidence and some sort of working thesis to change my mind.
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blog.mathoffthegrid.com/2019… I also went back. To this problem a few years back and blogged about it. I tend to work in small spurts in the evening rather than one long block.
Timothy Gowers @wtgowers@wtgowers17 Jul 2023
From time to time I have posted videos on YouTube of myself solving maths problems in real time. Here are some more, with the difference that they are six videos all devoted to the same problem, with a total length of around five hours. 1/ youtube.com/watch?v=fl4xw829…

A hard problem in elementary geometry

This is a beautiful problem that looks at first like a simple case ...

youtube.com
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threads.net/t/Cue0QR5LAV2 Is the pond drying up?
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That echoes my impression this morning . There was the most activity to look at after breakfast than I've seen yet.
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Benjamin Leis retweeted
Yuri Kazakov@kazakov_yu19 Jun 2023
Replying to @benjamin_leis
Two Pifagor theorems for blue triangles solve this problem.
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The cosine reverse power reduction triangle
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Benjamin Leis retweeted
Akiva Weinberger@akivaw12 Jun 2023
Replying to @therealjrbrown @benjamin_leis @divbyzero
This is a theorem of Niven, and the answer is yes
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Puzzle I came up with based on a riff on a recent ARML problem.
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Formulas are useful for reducing computational load when doing the same calculation but they also make it easier to extend the learning. If you continually have to go back to first principles for everything, you rarely can move beyond.+
Paige@MrsSheehanMath6 May 2023
Math teachers: I’d love opinions on this. I didn’t teach my kids an explicit formula for permutations or combinations this year. We used logic to find the solutions and looked for patterns. Should I being showing them the explicit formulas? #mtbos #iteachmath
54%Yes, show them!
46%No, they don’t need them
154 votes • Final results
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But I also find deriving the formulas has its own intrinsic value in terms of understanding.
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Replying to @mathssolutionz
@mathssolutionz
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You apparently can't reply to this post due to the substack link. Anyway highly recommended. Hopefully @JDHamkins adds a mastodon presence
Joel David Hamkins
@JDHamkins8 Apr 2023
Replying to @JDHamkins
joeldavidhamkins.substack.co…

Infinitely More | Joel David Hamkins | Substack

The mathematics and philosophy of the infinite. Click to read Infinitely More, by Joel David Hamkins, a Substack publication with tens of thousands of subscribers.

infinitelymore.xyz
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Lacking a printer, I need to find out a way to have someone do this for me.
Math for Love@MathforLove7 Apr 2023
The 3d printing options on the new einstein are getting pretty awesome
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In light of the continued weirdness here: I'm also on mastodon @benleis@mathstodon.xyz . This is a great time to try it out.
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