GOMBOC: THE SHAPE THAT CANNOT EXIST

     

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  Consider an egg. You can balance it on one of its ends. It won't last long. The slightest disturbance will topple it. The two tips of the egg are known as unstable equilibrium points. "Equilibrium" because you can balance the egg on them and 'unstable' because the egg will fall over at the slightest nudge. The points around the egg's body on which it balances robustly are called 'stable equilibrium' points.

     Now consider a flat square (a cardboard piece). It has four 'stable equilibrium' points at the center of the sides. You can balance that square on these points. It also has four unstable equilibrium points at its corners. Similarly, a triangle has three stable and unstable equilibrium points. All ellipse has two stable equilibrium points in the centers of its long side and two unstable ones at the ends.

    Can you find a two or three-dimensional shape that is convex(that is like full coconut, and not like broken half of the coconut) and homogeneous (uniform density) that has one stable and one unstable equilibrium point? The answer is bold "NO".

    The three-dimensional object which satisfies the above conditions is called GOMBOC. It does not exist naturally. Artificial Combocs have been made (see video).  It somewhat looks like an egg with many surfaces. If you put it on any of its sides it will turn, move, struggle, and ultimately come and rest on its only stable equilibrium point. It is a 'self-righting body'. The Tanjore doll (Tamil Nadu, India) is somewhat similar to GOMBOC. But it does not meet the conditions like convex and homogeneous.

    On a sea-shore, pebbles are present in all shapes. But no Gomboc is found in them. Gomboc pebble might have been made. But It had only a short life. It might have been chipped into ordinary pebble quickly. Because Gomboc strictly requires perfect shape. Even a slight disturbance in the shape will transfer Gomboc into a Non-Gomboc object.

    Some turtles have nearly Gomboc shape. But not a perfect one.  If they turn upside down, they can be erect again with little pushes here and there. So we can say,' turning turtle and then turning Gomboc'.

     There is a website dedicated to Gomboc. It sells Gomboc as gift items. It costs around 200 euros.

GOMBOC: Yet another peculiar shape.