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@samjshah.bsky.social

high school math teacher! #mtbos

266 Posts454 Follower360 Folgt
Dave Richeson@divbyzero.bsky.social · 2mo ago

Here are a few more curved origami pieces I made. Technically, I made them so the crease lies in the same plane. But if I make the strips narrow enough relative to the object's size, you can get the over-and-under behavior to work pretty well. I could have made all of these except the 5₁ knot

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Jim Simons@pippinsboss.bsky.social · 2mo ago

I like the proof using complex numbers, which is how Van Aubel himself proved it (using the strange notation where √ as a stand-alone symbol means what we call i). You might enjoy my video on the subject. youtu.be/pUSI91Mo7LU

Three pretty geometric theorems, proved by complex numbers

YouTube video by Jim Simons

youtu.be

ProfSmudge@profsmudge.bsky.social · 2mo ago

Van Aubel's Theorem (mentioned in Paul's report): the purple lines are equal and at right angles. The diagram, based on an article by Yutaka Nishiyama, provides the skeleton of a proof (nicer than Paul's proof based on vectors (in my view!)).

David K Butler@davidkbutler.bsky.social · 3mo ago

A deltahedron I made at #100factorial today with the polydron triangles. It’s a size-three octahedron with three size-one tetrahedra on each face. The whole shape has 120 faces, 180 edges and 62 vertices, with exactly 40% of the edges concave. It took me two hours to make, and some extra hands.

A 3D shape made out of plastic triangles clicked together at their edges. There are large sections each in a different colour, which are a big flat triangle three small triangles a side, three small triangles of which have been replaced with an outwards-facing pyramid. The colours visible in order of how much of it you can see are green, blue, black, purple, yellow and white. A piece of paper in front of the shape says Total faces: 15 times 8 =120 Convex edges: 180 minus 72 =108 Concave edges: 8 times 9 =72 Total edges: 120 times 3 halves =180 Total vertices: 180 minus 120 plus 2 =62 Percentage edges concave = 72 over 180 = 8 over 20 = 2 over 5 = 40%A 3D shape made out of plastic triangles clicked together at their edges. There are large sections each in a different colour, which are a big flat triangle three small triangles a side, three small triangles of which have been replaced with an outwards-facing pyramid. The colours visible in order of how much of it you can see are white, red, yellow, orange, blue and purple. A piece of paper in front of the shape says Total faces: 15 times 8 =120 Convex edges: 180 minus 72 =108 Concave edges: 8 times 9 =72 Total edges: 120 times 3 halves =180 Total vertices: 180 minus 120 plus 2 =62 Percentage edges concave = 72 over 180 = 8 over 20 = 2 over 5 = 40%
benjamin dickman@benjamindickman.bsky.social · 3mo ago

what a final @todos-math.bsky.social e-news message! congrats to @dingleteach.blacksky.app for her leadership of TOODS as she segues into Past President; congrats to @karikokka.bsky.social as incoming President; and congrats to two incoming Directors, including Dr. Sara Rezvi! 🔗 www.todos-math.org

Home - TODOS

At TODOS, we believe every student deserves access to mathematics that reflects their brilliance, culture, language and lived experience.

todos-math.org

benjamin dickman@benjamindickman.bsky.social · 4mo ago

working with students on problems of the nature: How many ways can you distribute 10 cookies among 3 people if the max # per person is m? For e.g. m = 4, you can ignore m and make the full list of all distributions. Then naively cross off every entry each time it contains an entry ≥ 5. But, then+

@samjshah.bsky.social · 5mo ago

I had a student who essentially needed something to yield 0 when positive and to yield 1 (or -1) when negative. They came up with this idea 💡 which was oh so lovely. #mtbos I love creativity and out of the box thinking.

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@samjshah.bsky.social · 5mo ago

I probably won’t be able to read this book (Proof: How the World Became Geometrical) for a while. But I thought the two other books by the author were great. And what a lovely cover! #mtbos

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Dave Richeson@divbyzero.bsky.social · 5mo ago

At Gathering 4 Gardner, @cardcolm.bsky.social suggested I try the following 3D-printing project. Recall the "napkin ring problem": Take a sphere of radius r and drill out a hole along a diameter so the remaining shape has height h. Then the volume, V = πh³/6, does not depend on R. He thought that

Four napkin rings of various radiiThe four napkin rings are the same height
Dave Richeson@divbyzero.bsky.social · 5mo ago

Another 3D-printing suggestion from @cardcolm.bsky.social: Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, it doesn't depend on where the slicing occurs. 1/2

A 3D-printed sphere sliced into equal-height pieces.
Carl@mathowitz.bsky.social · 5mo ago

I used to pride myself on writing questions that assessed what we had talked about, but in new & different ways. They'd get plenty of "the standard" questions, but I'd regularly mix in extension problems to see how they can apply their understanding. This was a favorite #mtbos #iteachmath

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Ayliean@ayliean.bsky.social · 5mo ago

Small Rhombicosidodecahedron if u even care. I know it can be made with a single (incredibly long) modelling balloon because every vertex only has four lines coming from it, so it has an ✨Eulerian path✨

Ayliean@ayliean.bsky.social · 5mo ago

Not sure what phase of my life I’m in, but here’s that modelling balloon icosidodecahedron nobody asked for! In theory it could be made out of a single modelling balloon, although in reality they don’t make balloons long enough :(