In the video it sounds more like an observation/prediction than an argument, I think? Like, "this will happen", not "I want this to happen".

But it's very possible that she has this opinion... and that would also explain why she made a video about this at all.

Does that count as 2 cuts ? @chrisstaecker.bsky.social 🤔

Then you can use the triangle BEF that you just cut away to measure on side AD where G should go, and make the third cut to point "I" using a hand square for the right angle.

Here is one with 3 cuts and no reflections. The grid is to scale specifically for the 9 x 13 case. It seems doable in practice: split the top edge at point E into lengths 6 and 7, then cut from that point to the bottom left corner. Then make a right angle at E for the second cut.

When you say "a calculus class"... Do they know line integrals, flux integrals, Green and Stokes?

I think if you only care about the feeling of hot/cold how we experience it in everyday life and don't have a more sophisticated physical definition (involving energy or particles), then it's completely symmetrical. We have nerve receptors for cold which send real signals (not absence of a signal)

Doesn't the "cold" just rush into the chemical bonds of the wood in the match? You could say an exothermic reaction absorbs cold, so you feel warmth.

Why stop there? The unit quaternions double cover 3D rotations, but the unit complex numbers can n-fold cover 2D rotations for any n! Just add a few more q's in there and you're off to glory

And there are left and right doors!

Also some slides and staircases

Ah, I found pieces with a single 45 degree angle that are chiral, like 6477749/5091

Someone should make a list of all the chiral Lego pieces (if there exist any!). Lots of heads and hair pieces are, but that doesn't prevent you from building anything mirror-imaged.

What are your favorite applications to teach in a first group theory course?

I really like burnside's lemma since it allows you to actually compute some things and doesn't have any other prerequisites.

Derivations are very elegant but I think it's equivalence classes of curves. It's also the closest to the way you actually compute things on concrete examples.