Balance Game
Wooden ‘Balance Game’ box
Game in play
The stall of wooden toys at my local market has this ‘Balancing Game’ currently on sale. The object is to place the wooden shapes on top of the hemisphere so that they do not fall over. The sequence in which the shapes are to be placed is determined by the throw of the die. It can be played competitively or as a sort of ‘solitaire’.
As the shapes are added so the centre of gravity of the structure rises. Theoretically it will become unstable and fall over once the centre of gravity is raised above the centre of the sphere.
It would be an interesting exercise for a mathematical sixth–former, given the masses and dimensions of the shapes, to calculate how many shapes can be added before this occurs.
According to my calculations it should not be possible to balance all the shapes, even starting with the largest at the bottom. Yet, as the photo shows, it can be done – on a suitable surface! I think the ‘give’ in the table covering might be the reason physics is defied. Also, the hemisphere, being turned in wood, may not be truly spherical.
Anyway it is fun.