4 ms·

The GömböC: An object that shouldn't exist (2014)

115 points by mhb 5y ago

neonate 5y ago
https://web.archive.org/web/20220321222926/https://plus.maths.org/content/gomboc-object-barely-exists https://web.archive.org/web/20220321222926/https://plus.math...
holistio 5y ago
Hungarian here! The Gömböc is awesome, I have a small aluminium one on my bookshelf. You can get one here, I think they (I'm not affiliated) ship internationally: https://gomboc-shop.com/ https://gomboc-shop.com/
- gregoryl 5y ago
  The Gömböc business has quite the margin. 290 euro for an aluminum one. Plus shipping!
  - Cthulhu_ 5y ago
    Only a matter of time before Chinese manufacturers start making these en masse as desk toys, they just need a spurt of popularity.
  - epivosism 5y ago
    Have 3d printed ones shown up yet? Can't wait, would love to play with one. Searched for this a few years ago but with no luck.
    - bitexploder 5y ago
      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.
      - skykooler 5y ago
        I suspect these would work much better on an SLA printer, as the result is a) homogenous/solid and b) much smoother than something off an FDM printer.
    - cshimmin 5y ago
      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..
      - bitexploder 5y ago
        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.
    - holistio 5y ago
      They have plastic ones now for 79 euros. I would have probably bought one of those had they appeared earlier.
    - ur-whale 5y ago
      >Have 3d printed ones shown up yet? https://www.thingiverse.com/thing:1985100 https://www.thingiverse.com/thing:1985100
    - microtherion 5y ago
      There are a few models on thingiverse, and one of them comes with some interesting claims: https://www.thingiverse.com/thing:10190 https://www.thingiverse.com/thing:10190 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.
  - drakonka 5y ago
    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?
  - deleted 5y ago
    [deleted]
- radarsat1 5y ago
  From the video on that site: > "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.
mattkrause 5y ago
Despite the title, gömböcs do exist in nature. 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-living-g-mb-c https://www.naturalhistorymag.com/biomechanics/10309/the-liv...
- cshimmin 5y ago
  Well, in the mathematical sense that's not true. The Gomboc is defined as a homogeneous solid object with one stable equilibrium.
  - mattkrause 5y ago
    The article gets into that at the very end: the lungs are near the top of the tortoise, which also helps it flip back onto its feet. I wasn't really taking issue with the post title; I just thought it was an excuse to share something that I thought was pretty neat :-)
  - Lerc 5y ago
    Well It's homogeneous in the sense that it's turtles all the way through.
    - positus 5y ago
      Hilarious — thank you.
notacoward 5y ago
Pronunciation guide (three samples): https://forvo.com/word/g%C3%B6mb%C3%B6c/ https://forvo.com/word/g%C3%B6mb%C3%B6c/
kazinator 5y ago
Dollars to doughnuts is a too-worn-out phrase. Proposed replacement: "Gömböcs to Mömbius strips says its true ..." "If it's three platinum Gömböcs to my two rubber Mömbius strips, you're on." "I'm so confident I will throw in a hand-blown Klein bottle."
- tempodox 5y ago
  I already have a hand-blown Klein bottle :) https://www.kleinbottle.com https://www.kleinbottle.com
rob74 5y ago
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 https://en.wikipedia.org/wiki/Head_cheese), which is traditionally filled into the pig's stomach and therefore also has a round-ish shape.
- kaba0 5y ago
  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”
  - bbotond 5y ago
    YouTube link for anyone interested: https://www.youtube.com/watch?v=sSnAbMhMeHs https://www.youtube.com/watch?v=sSnAbMhMeHs I had nightmares after watching this as a kid.
  - jrochkind1 5y ago
    > whose job is to keep/check on pigs (don’t know the English word) "swineherd" but it's an uncommon/archaic word in at least American English, and most people would just say what you said.
  - zgiber 5y ago
    “in LIFO order” - made my lunch break
ur-whale 5y ago
https://www.thingiverse.com/thing:1985100 https://www.thingiverse.com/thing:1985100
jankovicsandras 5y ago
While we are at cool mathematical objects discovered by hungarians, I really like the Szilassi polyhedron: https://en.wikipedia.org/wiki/Szilassi_polyhedron https://en.wikipedia.org/wiki/Szilassi_polyhedron This and the tetrahedron are the only two known polyhedra in which each face shares an edge with each other face.
raldi 5y ago
> They then proved that a Gömböc's flatness and thinness both have to be equal to 1, that is, both values have to be as small as is possible. I don’t get this. The shape in the video looks neither flat nor thin.
- regularfry 5y ago
  It's the other way round. Flatness and thinness are values greater than or equal to 1, so a shape with a flatness of 1 is minimally flat.
shireboy 5y ago
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.
- actually_a_dog 5y ago
  Assuming that by "teardrop shape," you mean the thing shown in [0], it would be stable sitting on the round end, as well as sitting on its side. --- [0]: https://www.turbosquid.com/3d-models/obj-teardrop/745957 https://www.turbosquid.com/3d-models/obj-teardrop/745957
- bzax 5y ago
  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.
- RugnirViking 5y ago
  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

115 points by mhb 5y ago

https://web.archive.org/web/20220321222926/https://plus.maths.org/content/gomboc-object-barely-exists https://web.archive.org/web/20220321222926/https://plus.math...

holistio 5y ago

Hungarian here! The Gömböc is awesome, I have a small aluminium one on my bookshelf. You can get one here, I think they (I'm not affiliated) ship internationally: https://gomboc-shop.com/ https://gomboc-shop.com/

gregoryl 5y ago
The Gömböc business has quite the margin. 290 euro for an aluminum one. Plus shipping!
- Cthulhu_ 5y ago
  Only a matter of time before Chinese manufacturers start making these en masse as desk toys, they just need a spurt of popularity.
- epivosism 5y ago
  Have 3d printed ones shown up yet? Can't wait, would love to play with one. Searched for this a few years ago but with no luck.
  - bitexploder 5y ago
    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.
    - skykooler 5y ago
      I suspect these would work much better on an SLA printer, as the result is a) homogenous/solid and b) much smoother than something off an FDM printer.
  - cshimmin 5y ago
    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..
    - bitexploder 5y ago
      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.
  - holistio 5y ago
    They have plastic ones now for 79 euros. I would have probably bought one of those had they appeared earlier.
  - ur-whale 5y ago
    >Have 3d printed ones shown up yet? https://www.thingiverse.com/thing:1985100 https://www.thingiverse.com/thing:1985100
  - microtherion 5y ago
    There are a few models on thingiverse, and one of them comes with some interesting claims: https://www.thingiverse.com/thing:10190 https://www.thingiverse.com/thing:10190 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.
- drakonka 5y ago
  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?
- deleted 5y ago
  [deleted]
radarsat1 5y ago
From the video on that site: > "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.

mattkrause 5y ago

Despite the title, gömböcs do exist in nature. 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-living-g-mb-c https://www.naturalhistorymag.com/biomechanics/10309/the-liv...

cshimmin 5y ago
Well, in the mathematical sense that's not true. The Gomboc is defined as a homogeneous solid object with one stable equilibrium.
- mattkrause 5y ago
  The article gets into that at the very end: the lungs are near the top of the tortoise, which also helps it flip back onto its feet. I wasn't really taking issue with the post title; I just thought it was an excuse to share something that I thought was pretty neat :-)
- Lerc 5y ago
  Well It's homogeneous in the sense that it's turtles all the way through.
  - positus 5y ago
    Hilarious — thank you.

notacoward 5y ago

Pronunciation guide (three samples): https://forvo.com/word/g%C3%B6mb%C3%B6c/ https://forvo.com/word/g%C3%B6mb%C3%B6c/

kazinator 5y ago

Dollars to doughnuts is a too-worn-out phrase. Proposed replacement: "Gömböcs to Mömbius strips says its true ..." "If it's three platinum Gömböcs to my two rubber Mömbius strips, you're on." "I'm so confident I will throw in a hand-blown Klein bottle."

tempodox 5y ago
I already have a hand-blown Klein bottle :) https://www.kleinbottle.com https://www.kleinbottle.com

rob74 5y ago

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 https://en.wikipedia.org/wiki/Head_cheese), which is traditionally filled into the pig's stomach and therefore also has a round-ish shape.

kaba0 5y ago
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”
- bbotond 5y ago
  YouTube link for anyone interested: https://www.youtube.com/watch?v=sSnAbMhMeHs https://www.youtube.com/watch?v=sSnAbMhMeHs I had nightmares after watching this as a kid.
- jrochkind1 5y ago
  > whose job is to keep/check on pigs (don’t know the English word) "swineherd" but it's an uncommon/archaic word in at least American English, and most people would just say what you said.
- zgiber 5y ago
  “in LIFO order” - made my lunch break

ur-whale 5y ago

https://www.thingiverse.com/thing:1985100 https://www.thingiverse.com/thing:1985100

jankovicsandras 5y ago

While we are at cool mathematical objects discovered by hungarians, I really like the Szilassi polyhedron: https://en.wikipedia.org/wiki/Szilassi_polyhedron https://en.wikipedia.org/wiki/Szilassi_polyhedron This and the tetrahedron are the only two known polyhedra in which each face shares an edge with each other face.

raldi 5y ago

> They then proved that a Gömböc's flatness and thinness both have to be equal to 1, that is, both values have to be as small as is possible. I don’t get this. The shape in the video looks neither flat nor thin.

regularfry 5y ago
It's the other way round. Flatness and thinness are values greater than or equal to 1, so a shape with a flatness of 1 is minimally flat.

shireboy 5y ago

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.

actually_a_dog 5y ago
Assuming that by "teardrop shape," you mean the thing shown in [0], it would be stable sitting on the round end, as well as sitting on its side. --- [0]: https://www.turbosquid.com/3d-models/obj-teardrop/745957 https://www.turbosquid.com/3d-models/obj-teardrop/745957
bzax 5y ago
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.
RugnirViking 5y ago
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