I learned in college Geometry class that you can transform a square to an equilateral triangle in 11 cuts or so
So I wrote a matlab program to draw the shapes, and cut them out, and it works
It’s mathematically exact, not just approximate
Still surprises me after 20 years, so I want to find this old program again lol
The dissection of a square into an equilateral triangle (or vice versa) is sometimes known as the haberdasher's problem, and can be done in three straight-line cuts.
https://mathworld.wolfram.com/HaberdashersProblem.html
Hm interesting, I thought it was 11 pieces, not 11 cuts, but that one looks like 4 pieces, which is surprising
Now I am more curious to find this program
Either I didn't do it optimally, or there is some variation like a triangle/rectangle/square
I think there are some problems that have 3 shapes, or it could be triangle/pentagon or something
TIL that Gavin Theobald has produced several dissections from a triangle to a square on the surface of a sphere. Which would make pretty cool 3D-printed desk gizmos: make a ball with a triangular sector removed from one pole, a square sector removed from the other pole, and a set of wedge-shaped pieces that can be used to fill up either hole.
http://www.gavin-theobald.uk/HTML/Spherical/T90-S112.5.pdf
http://www.gavin-theobald.uk/HTML/Spherical/T100-S120.pdf
http://www.gavin-theobald.uk/HTML/Spherical/T120-S135.pdf
http://www.gavin-theobald.uk/HTML/Spherical.html
This got a downvote and I wonder if it’s from a person who doesn’t think it’s true
Or perhaps from someone who doesn't think it's useless
It more likely s from a person whose fingers are much larger than the distance between the up/downvote triangles on their device (that’s about everybody)
Indeed, although note that if you do fat-finger the up or down vote button, you can undo that by poking the 'unvote' or 'undown' link that appears on the same line.
Some men just want to watch the world burn.