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A puzzle that tiles infinitely across both sides, based on the Klein Bottle

n-e-r-v-o-u-s.com

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Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#31

Post by zodPod »

NickBusey wrote: post #27
zodPod wrote: post #26

Earlier quoted context omitted.

Agreed? I mean, I think my comment makes it clear this way too expensive premium market isn't really the demographic that I fit into, though I know you're trying to prove a point. I do find it a little annoying that the internet has made it common to price based on the people who will pay the most for things. It is still just cardboard. Just because it's an interesting idea doesn't necessarily make 236 pieces of card…

To counter your point, it is not just cardboard. It is laser cut wood. A far more expensive material, and manufacturing process.

Fair point sorry I totally missed that. I still think it's too pricey but you're right that that is a more expensive material and definitely deserves to be reasonably more expensive.

Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#32

Post by gnarbarian »

AKrumbach wrote: post #16
gnarbarian wrote: post #9

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.

Woah, Thanks! Does the AK in your name stand for Alaska? If so, I'm in Anchorage.

Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#34

Post by gnarbarian »

tobr wrote: post #33

Could someone who understands the topology of this more fully say - if I had a set of two or more of these, could I solve each separately and put the solved puzzles together into a larger pattern?

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/...

Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#35

Post by tobr »

gnarbarian wrote: post #34
tobr wrote: post #33

Could someone who understands the topology of this more fully say - if I had a set of two or more of these, could I solve each separately and put the solved puzzles together into a larger pattern?

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...

Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#36

Post by gnarbarian »

tobr wrote: post #35
gnarbarian wrote: post #34

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...

well if anything from the left side can be flipped 180 and attached to the right side of the klein puzzle you should be able to assemble two copies in the same configuration, then flip one whole puzzle over 180 and attach it to the side of the other.

Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#39

Post by pgreenwood »

chris_st wrote: post #37

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?

No cross-caps here. The first puzzle is a torus, the second a Klein bottle. Informally: the Klein bottle has on pair of edges is glued with a twist and one without; with the cross-cap, both pairs of edges are twisted then glued.

Re: A puzzle that tiles infinitely across both sides, based on the Klein Bottle

#40

Post by emmelaich »

tempodox wrote: post #12
mcherm wrote: post #10

Earlier quoted context omitted.

That would be INCREDIBLY awesome, considering that it would require pieces that have a curve in to the 4th dimension (or perhaps just pieces that could pass through each other). A Klein bottle is a 2-dimensional surface cannot be embedded in a 3-dimensional space without crossing.

While this is true mathematically, there is at least one project that emulates Klein bottles in 3D quite credibly: http://www.kleinbottle.com Edit: You can even put in some liquid (the “hose” continues through the crossing). The fun part is getting it out again :)

Hey that's the famous Clifford Stoll of Cuckoo's Egg fame.

Glad he is not famous only for that book. As fine as it is.

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