7 ms·

Gömböc

113 points by kaffeemitsahne 8y ago

zokier 8y ago
For such a fascinating shape you'd think that there would be at least one video, picture, or even illustration of it sitting on its unstable equilibrium point. It is also interesting how this particular shape seems to have strong marketing campaign behind it. It is not everyday you see mathematical concepts perk up commercial interest.
- joshschreuder 8y ago
  There is a gif I think, unless I'm misunderstanding: https://en.m.wikipedia.org/wiki/File:G%C3%B6mb%C3%B6c.gif https://en.m.wikipedia.org/wiki/File:G%C3%B6mb%C3%B6c.gif
  - soheil 8y ago
    If the object is moving it is not in an equilibrium position.
    - joshschreuder 8y ago
      I did misunderstand :) It would be interesting to see what the GP is describing.
    - gisely 8y ago
      An object can move through an equilibrium position due to momentum, no? Being an stable equilibrium position just means that slight perturbations from that position will be reduced by the forces acting on it. An unstable equilibrium means any perturbation away from the position will be increased-- thus the object may pass close to this point, but will never stay at because even the smallest deviation would cause it to leave.
- WhiteSage 8y ago
  The unstable point is at the top of the crest. You would need a vacuum chamber with dampened vibrations to have any chance of it standing there, as any small deviation from a perfectly balanced position would make it fall.
  - fromthestart 8y ago
    Under ideal theoretical conditions, yes. In practice, friction and material deformation will probably give the top of the crest some degree of stability, possibly enough for a demonstration. At the very least it will probably be much slower to roll from such a metastable orientation. Edit: also, based on the following gif someone else posted, I don't think the top of the crest is the metastable point. You can see the object linger at that point before seemingly spontaneously finding true equilibrium - illustrating my point rather well. https://en.m.wikipedia.org/wiki/File:Gömböc.gif https://en.m.wikipedia.org/wiki/File:Gömböc.gif
  - derefr 8y ago
    You could also just build a version of the object with an internal accelerometer and motor milled into it, that work together against torque. This would make the point of unstable equilibrium into a point of dynamic equilibrium, like a modern jet fighter, or a human being using their core to support their weight, or a hoverboard (but in more dimensions.)
- sorokod 8y ago
  Some here https://vimeo.com/51887199 https://vimeo.com/51887199
pgtan 8y ago
There was a lecture on the long science night fest here about the Gömböc.¹ A very interesting observation accompanying the idea of the Gömböc is, that the number of stable and unstable equilibrium points decreases, the more a stone travels along a river. ¹ https://www.mis.mpg.de/wissenschaftsnacht2016/programm-im-vortragsraum/gleichgewicht.html https://www.mis.mpg.de/wissenschaftsnacht2016/programm-im-vo...
cpach 8y ago
Fascinating! If anyone would like to have their own gömböc, there is a web shop here: https://gomboc-shop.com https://gomboc-shop.com
- harshreality 8y ago
  > Each Gömböc comes with a booklet containing every necessary information about the product, as well as a unique product ID to identify the Gömböc and prove its authenticity. Sandblasted Al: 239 Euro Porcelain: 606 Euro Steel: 499 Euro Bronze: 599 Euro Plexiglass: 199 Euro Polished Al: 269 Euro Al (rough polish): 199 Euro Black (polyoxymethylene): 249 Euro https://www.google.com/search?q=gomboc+3d+model https://www.google.com/search?q=gomboc+3d+model I'm guessing it costs an order of magnitude less than those published prices to machine an aluminum one, given an accurate model? The product page says the Al one is 500g, so the machining cost is probably the most significant factor?
  - Al-Khwarizmi 8y ago
    Strange, I was looking for gömböcs this morning (like 12 hours ago) and now I find them in the HN front page. I found this website which has much cheaper gömböcs (42 €): http://gomboc-online.com/index.php/gomboc.html http://gomboc-online.com/index.php/gomboc.html But apparently their only shipping method that ships outside Hungary is "currently unavailable". Well, there is also the option "SZEMÉLYES ÁTVÉTEL GLS CSOMAGPONTON" but Google is not very concrete when translating it. It sounds to me like picking up in a "something-point" though, which also looks like it's not international shipping. If anyone keeps investigating and finds a gömböc that wouldn't make me broke and can ship without shenanigans outside of Hungary, I'd be grateful.
    - kowdermeister 8y ago
      > SZEMÉLYES ÁTVÉTEL GLS CSOMAGPONTON Means that you can pick it up personally at a GLS (like FedEx) point. The checkout page does say it ships internationally: "DHL EXPRESS WORLDWIDE"
tinus_hn 8y ago
I don’t really understand why an egg shape does not satisfy the requirements.
- throwaway2048 8y ago
  think of an egg on its side, it can rest anywhere along it

For such a fascinating shape you'd think that there would be at least one video, picture, or even illustration of it sitting on its unstable equilibrium point. It is also interesting how this particular shape seems to have strong marketing campaign behind it. It is not everyday you see mathematical concepts perk up commercial interest.

joshschreuder 8y ago
There is a gif I think, unless I'm misunderstanding: https://en.m.wikipedia.org/wiki/File:G%C3%B6mb%C3%B6c.gif https://en.m.wikipedia.org/wiki/File:G%C3%B6mb%C3%B6c.gif
- soheil 8y ago
  If the object is moving it is not in an equilibrium position.
  - joshschreuder 8y ago
    I did misunderstand :) It would be interesting to see what the GP is describing.
  - gisely 8y ago
    An object can move through an equilibrium position due to momentum, no? Being an stable equilibrium position just means that slight perturbations from that position will be reduced by the forces acting on it. An unstable equilibrium means any perturbation away from the position will be increased-- thus the object may pass close to this point, but will never stay at because even the smallest deviation would cause it to leave.
WhiteSage 8y ago
The unstable point is at the top of the crest. You would need a vacuum chamber with dampened vibrations to have any chance of it standing there, as any small deviation from a perfectly balanced position would make it fall.
- fromthestart 8y ago
  Under ideal theoretical conditions, yes. In practice, friction and material deformation will probably give the top of the crest some degree of stability, possibly enough for a demonstration. At the very least it will probably be much slower to roll from such a metastable orientation. Edit: also, based on the following gif someone else posted, I don't think the top of the crest is the metastable point. You can see the object linger at that point before seemingly spontaneously finding true equilibrium - illustrating my point rather well. https://en.m.wikipedia.org/wiki/File:Gömböc.gif https://en.m.wikipedia.org/wiki/File:Gömböc.gif
- derefr 8y ago
  You could also just build a version of the object with an internal accelerometer and motor milled into it, that work together against torque. This would make the point of unstable equilibrium into a point of dynamic equilibrium, like a modern jet fighter, or a human being using their core to support their weight, or a hoverboard (but in more dimensions.)
sorokod 8y ago
Some here https://vimeo.com/51887199 https://vimeo.com/51887199

pgtan 8y ago

There was a lecture on the long science night fest here about the Gömböc.¹ A very interesting observation accompanying the idea of the Gömböc is, that the number of stable and unstable equilibrium points decreases, the more a stone travels along a river. ¹ https://www.mis.mpg.de/wissenschaftsnacht2016/programm-im-vortragsraum/gleichgewicht.html https://www.mis.mpg.de/wissenschaftsnacht2016/programm-im-vo...

cpach 8y ago

Fascinating! If anyone would like to have their own gömböc, there is a web shop here: https://gomboc-shop.com https://gomboc-shop.com

harshreality 8y ago
> Each Gömböc comes with a booklet containing every necessary information about the product, as well as a unique product ID to identify the Gömböc and prove its authenticity. Sandblasted Al: 239 Euro Porcelain: 606 Euro Steel: 499 Euro Bronze: 599 Euro Plexiglass: 199 Euro Polished Al: 269 Euro Al (rough polish): 199 Euro Black (polyoxymethylene): 249 Euro https://www.google.com/search?q=gomboc+3d+model https://www.google.com/search?q=gomboc+3d+model I'm guessing it costs an order of magnitude less than those published prices to machine an aluminum one, given an accurate model? The product page says the Al one is 500g, so the machining cost is probably the most significant factor?
- Al-Khwarizmi 8y ago
  Strange, I was looking for gömböcs this morning (like 12 hours ago) and now I find them in the HN front page. I found this website which has much cheaper gömböcs (42 €): http://gomboc-online.com/index.php/gomboc.html http://gomboc-online.com/index.php/gomboc.html But apparently their only shipping method that ships outside Hungary is "currently unavailable". Well, there is also the option "SZEMÉLYES ÁTVÉTEL GLS CSOMAGPONTON" but Google is not very concrete when translating it. It sounds to me like picking up in a "something-point" though, which also looks like it's not international shipping. If anyone keeps investigating and finds a gömböc that wouldn't make me broke and can ship without shenanigans outside of Hungary, I'd be grateful.
  - kowdermeister 8y ago
    > SZEMÉLYES ÁTVÉTEL GLS CSOMAGPONTON Means that you can pick it up personally at a GLS (like FedEx) point. The checkout page does say it ships internationally: "DHL EXPRESS WORLDWIDE"

tinus_hn 8y ago

I don’t really understand why an egg shape does not satisfy the requirements.

throwaway2048 8y ago
think of an egg on its side, it can rest anywhere along it