21–30 of 53 posts
I want to see a jigsaw puzzle that results in a mobius strip.
I don't see how this is based on a Klein Bottle.
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.
I can buy a 1000 piece puzzle for $5 at walmart. Sure it's not nearly as cool as this but 236 pieces for $120? That's outrageous. I'd rather just have my money, thanks.
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.
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 :)
There are lots of projects that do this (implement a Klein bottle with a crossing).
I can buy a 1000 piece puzzle for $5 at walmart. Sure it's not nearly as cool as this but 236 pieces for $120? That's outrageous. I'd rather just have my money, thanks.
I can buy a 1000 piece chicken McNuggets for $5 at McDonalds. Sure it's not nearly as cool as a fresh local meal from a nice restaurant, but dinner for 2 for $120? That's outrageous. I'd rather just have my money, thanks.
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 cardboard worth $120.
To counter your point, this is like paying $120 for chick-fil-a nuggets instead of $5 for McDonald's nuggets. It's still just cardboard. It's slightly better made cardboard with maybe a little extra care, but it's just cardboard.
Earlier quoted context omitted.
I can buy a 1000 piece chicken McNuggets for $5 at McDonalds. Sure it's not nearly as cool as a fresh local meal from a nice restaurant, but dinner for 2 for $120? That's outrageous. I'd rather just have my money, thanks.
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…
I don't see how this is based on a Klein Bottle.
Every closed surface comes from a symmetry of the sphere, the Euclidean plane, or the hyperbolic plane. For instance, you can get a (flat) torus by taking the Euclidean plane and taking all translations that shift the plane in the x and y directions by integer amounts, where we consider two points to be "the same" if they are translates of each other. So, if you take a path horizontally, you periodically return to "the same" point every unit distance. This is the Asteroids geometry.
The Klein bottle can be obtained by the symmetry generated by two transformations: (1) a vertical translation by 1 unit and (2) a horizontal translation by 1 unit followed by a vertical flip.
The wooden puzzles are from tiling the plane in a way that respects one of these symmetries, and then taking just enough puzzle pieces to cover the fundamental domain. For the Klein bottle, all this together means that in one direction you can take off a piece and put it down on the other side in the same orientation, and in the other direction you have to flip the piece over.
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.