The shells of some tortoises are gömböc-shaped, with the only stable configuration being feet-down/right-side up. This makes it easier for the animal to right itself if it somehow lands on its back.
Some linguistic context: gombóc means "dumpling" in Hungarian, and gömböc itself is a less commonly used name for head cheese (https://en.wikipedia.org/wiki/Head_cheese), which is traditionally filled into the pig's stomach and therefore also has a round-ish shape.
There is also a Hungarian folk tale titled “little gömböc” where a poor family gets hungry and the father sends their daughter up to the attic to bring down the head cheese, but instead the latter eats the girl. After she disappears the father sends the other 2 girls, then his wife, then himself all of them disappearing into the ever-expending stomach of the not-so-little Gömböc, which at this point get so heavy that it falls onto the ground and rolls out the house, eating everyone in its way, including the whole village.
Fortunately the boy whose job is to keep/check on pigs (don’t know the English word) has a knife in his pocket, cuts the Gömböc out from the inside and the whole village escapes in LIFO order. “And they lived happily ever after or something like that”
Looking at the webshop, I don't understand how they can justify these prices. Yes the object is cool, but in its physical form as sold here it would pretty much function as a fidget toy. Is it somehow expensive or very difficult to manufacture with the required balance attributes?
I would think the print layer resolution would spoil the effect since it would produce non-convex regions and extra equilibrium points. It could be smoothed by post-processing, but presumably polishing/sanding would get you into the same trouble. The article goes into how the shape "almost doesn't exist", which would seem to imply great precision is required. I'm wondering how they manage to machine the shape in metal..
Large print size helped. Highest resolution. We filed down a few imperfections very carefully with a lot of testing as went and got one that worked well. It has to be very precise.
My wife printed a few. They have to be relatively precise and it helps for them to be heavier than plastic so they react better. It is mostly disappointing and does not work without a lot of tweaking.
The model's creator says his design was essentially eyeballed because (at least in 2011) there existed no peer reviewed publication describing the actual shape of the Gömböc, making this more of a commercial enterprise than a mathematical discovery. He also appears to have had some dustups with the Gömböc discoverers over his claims who did not appreciate him posting his model.
It was not clear to me from the Wikipedia page what the real situation is. Is there currently a published description of the exact shape of a Gömböc? It would indeed be curious if there were not.
> "People from the western world always ask first what this is good for, but eastern people appreciate the beauty itself, and they want to understand the philosophy rather than the purpose of a shape like this."
As someone from the "western world", I suddenly don't want to buy anything from this guy, as amusing and interesting as his product may be. Insulting half your potential audience is not a great way to make sales.
Can some more mathy person (in laymen terms) explain how a teardrop shape (ie pointy at top, round at bottom) isn’t the same thing? Seems like that would just have one stable and one unstable point, though I’m sure I’m missing something.
unless you have an uneven weight distribution within the teardrop you can set it on its side no? The condition here is that the volume has an even mass distribution. Even if the teardrop resists being placed on its side, it seems to me that at some point along the side you must have a ring beyond which it falls the other way. The boundary would therefore consist of a ring of many unstable points
The teardrop side is probably either very pointy (in which case the entire shape fails to be convex), or the teardrop is too heavy and the stable points are instead around the waist of the teardrop, with the tip hanging to the side and down.
The shells of some tortoises are gömböc-shaped, with the only stable configuration being feet-down/right-side up. This makes it easier for the animal to right itself if it somehow lands on its back.
More here: https://www.naturalhistorymag.com/biomechanics/10309/the-liv...