Ran across an interesting bit of mathematics news this morning…
I happened to be working on a project that involves hex tiling, so it was easy to create an SVG of the einstein (literally “one stone” in German) tile for your cutting/engraving pleasure.
Right-click on the image above and “save as” an SVG.
Enjoy!
This seems perfect for scrap use! Just cut a bunch of these and tile them to make something cool!
ok, now this may be my next puzzle pattern.
There is also a project on the Cuttle site.
This is super cool. It’s the perfect random, weird shape to cut out of scrap.
A couple of people on Mastodon were showing off tiles they cut earlier. It was even one person’s first laser cutting project. Drawing in new people with math!
It’s called a Penrose pattern, discovered by Roger Penrose in 1974. Not sure what makes this recent “discovery” different. Veritasum put out a video 2 years ago about it, Numberphile 11 years ago, Matt Parker about 10 years ago, the Royal Institution, etc. Oxford University has a large section of paving that uses it outside the entrance to one of its buildings.
Still very cool, though.
I think what’s new is that it’s a single tile shape, where previous patterns needed more than one tile shape. But I’m mostly learning about this today 
Thanks!!! this was on my list to make and I hadn’t gotten to it yet. Appreciate the share.
Yes, exactly. Penrose needed two, this can do it with one.
Thank you for sharing. I love the look of this!
Aha! OK, I get it now! Thanks.
Just came here to post this, very cool indeed!
You are wicked!
Oh wow! Definitely going to try this. Thanks for the design!
Not fair! This is the same as using two different tiles, since some are flipped over with respect to the others. In my mind, that’s cheating and not really an improvement over Penrose’s solution.
Yup, puzzle pattern for sure in my future.
Dual side puzzle! Picture on both sides, to add to the complexity!
Same picture on both sides, just rotated or mirrored 
That was actually my first thought, but I then I figure that was TO mean.