Gömböc—The Shape That Shouldn't Exist

hey everyone today I'm going to be showing you the gum Bach the world's first self riding shape in order to understand how a gum Bach works we have to understand equilibrium points stable equilibrium and unstable equilibrium for example this is an unstable equilibrium you could if you got everything just perfect balance an egg on its end but it's really hard to do so this is called an unstable equilibrium and what happens in the unstable equilibrium is it always falls over and it goes to a stable equilibrium so on its side the egg is in a stable equilibrium so we have an unstable equilibrium unstable equilibrium stable and stable for a cuboid we have something similar so we have stable stable stable stable this is stable this is stable but on every corner we have an unstable equilibrium so the question is what's the minimum number of equilibrium points you can have on a 3d object well in 1995 a mathematician named vladimir arnold proposed that there's not a 3d object that currently exists that has less than four equilibrium points meaning if you add the stable and unstable equilibrium point you'll never find an object with less than four for example you can have this object here which seems like it only has one equilibrium point you can put it up top like this and it rolls over and ends up stable ii upside like this but this isn't just one equilibrium point this is actually at least four equilibrium points we have one stable equilibrium one unstable here one unstable here and one unstable here so that's four equilibrium points again but one Hungarian mathematician named Gabor de moco's who actually named this shape that gumbo he tried to prove that this object can exist and what he did is him and his wife collected a bunch of pebbles and he just rolled them on the ground and saw how many stable and unstable equilibrium points they had and saw if you could find any that had less than four and unfortunately that failed eventually though they were mathematically able to find a shape that existed that had only two equilibrium points one stable equilibrium and one unstable equilibrium point the gumbo is the world's first three dimensional convex and homogeneous shape that has only one stable and one unstable equilibrium point so this is its stable equilibrium point and this of course is is unstable equilibrium point and there's no other stable or unstable equilibrium point on this whole object besides those two now you may have seen something that always pops up like that there's toys that do this but the cool thing about the gun Bock is that it's a homogeneous shape meaning that it has the same density throughout the entire object so basically if you were to make an object that doesn't have the same density throughout it for example if I just put some weight on this tape roll here this will easily always write itself so I always come back to this point but in this case you're cheating because you've made it a non homogeneous shape but in this case there's no weights in this the entire thing can be made out of a solid material and it still behaves like this now the coolest thing I think about the gun Bock is that you'll notice that this may look similar to something that you've seen in nature a turtle now most Turtles right themselves just by wiggling their arms and legs and head around and they can eventually flip themselves over if they get turned over but some turtles have evolved the ability to flip themselves over using nothing but gravity and basically what they've evolved is a turtle shell that looks like this so if they get flipped over no matter how they land they can always write themselves if they just tuck everything in now there's only about three species of turtles that have evolved this way but it's amazing that they've evolved this exact same shape that mathematicians had to prove existed now it turns out a true gum buck is very hard to make because if it has any minor imperfections in it then it will create another unstable equilibrium point or even a stable equilibrium point and that's why the mathematician had such a hard time finding any objects that nature that are true gun box even the turtle that I mentioned isn't a true goong-bok but it's an imperfect one now these gun box that I have here are actually 3d printed if you want to make one I'll put the file that I use in my description hey everyone thanks for watching another episode of the action lab I hope you liked it if you did don't forget to subscribe if you haven't subscribed to my channel yet and you can also hit the bell so that you can be notified when I release my latest video and thanks for watching and I'll see you next time

Channel: The Action Lab

Views: 9,390,495

Rating: 4.9026289 out of 5

Keywords: Gömböc, gomboc, self-righting, shapes, geometry, shape shouldn't exist, shouldn't exist, the action lab, action lab

Id: rvVF5QWSYF4

Length: 5min 2sec (302 seconds)

Published: Fri Jun 12 2020