Mathematician. John J. & Ann Curley Chair in Liberal Arts at Dickinson College. Author of Tales of Impossibility and Euler's Gem. Coffee drinker. [Everything in the timeline before October 2024 was imported from my Twitter/X feed 2008-24.]
Dave Richeson
This is a big deal. It’s been an open question whether even billiards in a triangle always has a periodic orbit. Not surprised that all polygons would fall at once, however. The methods don’t even look too intimidating. Need to study this more carefully!
From yesterday to today, I figured out how to use my Silhouette cutting machine to score the cardstock. It makes the folding so much easier!
Let's see how this one goes. It should be an autostereogram movie (like an animated Magic Eye image). I wanted it to feel like The Matrix.
Also:
Joshua Bowman
Glimpse behind the curtain: I made it in Excel. Then I used conditional formatting to pick the colors. The random values change every time I make a change in the worksheet. So, I made changes at regular intervals and took a screen recording.
Borromean carabiners and Borromean paper clips.
Today I was reading about and playing with curved origami. Here's what I designed and made. It is cool how folding along the curve changes the shape of the object (like the M → ❤️).
Link to the book (which also has crease patterns that can be downloaded): mitani.cs.tsukuba.ac.jp/book/curved_...
Two different figure-eight knots made with curved origami. The blue one has a fold angle of 90°, and the purple has a fold angle of 60°. The latter can be made with one strip of paper. The former required two.
Here are a few more curved origami pieces. I've been reading _Curved-Folding Origami Design_ by Jun Mitani. The treble clef is his design. The trefoil is mine. I made the others, but they were based on photos in his book.
Giovanni Forni
Existence of a Periodic Orbit for Billiards in Polygons
https://arxiv.org/abs/2606.10102
