I, too, use both Desmos and Geogebra in my classroom. One of my favourite things about Geogebra is the ability to export to tikz. It can save a lot of time when making complex geometry problems while keeping things nice and neat in your latex file. I also like using the Geogebra 3D AR app to get kids to see the different ways planes intersect, and what a parameterized solution “looks like” in a 3x3 system. It makes for a lot of “aha” moments.
On the other hand Desmos is quick, easy to use, and looks nice. The test-mode app works well on phones and the College Board will be using it for their AP exams this year, so they must be doing something right. Their new 3D apps look promising but I haven’t played with them much, yet.
Both tools have their place, but my heart is 100% with Geogebra.
My odd claim to fame which is hard to garner praise for is that when I was a kid I always followed a certain pattern when I did something on a left or right foot. I always tried to even it out. So if I pinched my left toes, then I would do my right. But then I would undo that by going right then left. And then I would undo that by undoing the entire thing: right left left right. And the pattern went on:
LRRLRLLRRLLRLRRL…
and so on. It seemed easy enough to remember because you would just undo what you did last.
A few decades later and I learn that’s the Thue Morse word (1) which has many interesting properties like being overlap free. Unfortunately it didn’t give me any kind of advantage when studying combinatorics on words. Just a weird “wait… where have I seen this before?” moment.
I did the exact same thing, due to a feeling of wanting to "even" things out between right and left. Blew my mind that it was a known pattern; after watching this video: https://www.youtube.com/watch?v=prh72BLNjIk&t=549s
I'm always reminded that we are all more alike than we realise :)
I’ve found KDE Plasma to be quite stable. At least compared to Windows. I haven’t used macOS in quite a few years but AFAIC it’s pretty much impossible to beat that UI.
Maybe not surprising, but exciting! This kind of pessimistic take is what really surprises me. Crows can make mental templates, this is something we didn't know earlier, and is really neat, as far as I can tell.
Ahh, that would explain why the intersection of algebraic integers and Q is Z. I wasn’t convinced of that when I had the notion of algebraic numbers in place of algebraic integers.
I like teaching this kind of stuff to my grade 9 and 10 advanced math classes. It’s not that hard to understand and yet it gives students a sense of wonder about how math works. I might try to show the grade 10s algebraic integers now.
As a teacher who regularly rips off large expressions from textbooks and test generators with MathPix, this would allow me to also capture diagrams into my exercises.
