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

Joined January 2015
1,228 Photos and videos
Pinned Tweet
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
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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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.

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…
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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
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
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.
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
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But I also find deriving the formulas has its own intrinsic value in terms of understanding.
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Benjamin Leis retweeted
Replying to @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
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Lacking a printer, I need to find out a way to have someone do this for me.
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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