41–50 of 53 posts
this is awesome and reminds me of the tiling puzzle from the book Anathem: http://anathem.wikia.com/wiki/Teglon or https://en.wikipedia.org/wiki/Penrose_tiling I would love to have a Penrose tiling puzzle set.
I'm at work right now, but give me a day and I will design that.
https://hyperallergic.com/416579/engare-game-islamic-design/
this is awesome and reminds me of the tiling puzzle from the book Anathem: http://anathem.wikia.com/wiki/Teglon or https://en.wikipedia.org/wiki/Penrose_tiling I would love to have a Penrose tiling puzzle set.
I reverse-engineered the tiles in OpenSCAD. Let me know and I'll upload them.
This would be even more awesome if the puzzle pieces were curved, so they'd form a Klein bottle when put together.
This would be even more awesome if the puzzle pieces were curved, so they'd form a Klein bottle when put together.
Earlier quoted context omitted.
If you imagine the surface that is formed when every possible connection between pieces is made simultaneously, that surface is a Klein bottle. Obviously, making all the connections simultaneously is not possible in 3 dimensions, without allowing the pieces to deform and intersect each other.
Does that property imply a Klein bottle? I was not aware they were synonymous.
Earlier quoted context omitted.
I'm at work right now, but give me a day and I will design that.
Woah, Thanks! Does the AK in your name stand for Alaska? If so, I'm in Anchorage.
Anyway, "puzzle" is now available at https://drive.google.com/file/d/1KYDTZ2AVWQfWCSACUvfl5gAIHzA...
If I counted correctly, you should be able to make a roughly rectangular shape out of the provided pieces. (Even if I miscalculated, I think they make a good exploration toy for the P2 tiling anyway.)
So it's many (more than I want to admit :-) years since my Euclidean and Non-Euclidian Geometry class, but isn't this a cross-cap, not a Klein bottle?
Earlier quoted context omitted.
from the article: > Multiple infinity puzzles can be combined to create a larger continuous puzzle. The image above shows some of the creative combinations possible with two infinity puzzles of different colors ($75, for two). here is the image from the quote: https://i2.wp.com/n-e-r-v-o-u-s.com/blog/wp-content/uploads/...
Sorry! I should’ve both read and expressed myself more carefully. I meant the Klein bottle topology, not the torus. EDIT: FWIW torus puzzles are definitely not a new thing - I had this one as a kid: http://img.tradera.net/images/096/270662096_95a37033-d8f9-4c...
This would be even more awesome if the puzzle pieces were curved, so they'd form a Klein bottle when put together.
I think the flat version is a more authentic representation of the 4-dimensional object. If you were a 2D creature embedded in the surface of a Klein bottle, space would seem flat in every direction... at least until you went out for a walk and found the mirror-image of your house.