|Figure 1. An egg standing to attention.|
We start with a challenge (supposedly) set by Christopher Columbus. Whilst dining one night, a nobleman approached him and suggested that finding the Americas was not that impressive because anyone sailing out that way could not have missed them. In reply Columbus challenged the nobleman to take a normal egg and place it so it stood upright. Now, there are many ways of doing this, but most use some other piece of apparatus (such as alternating current), but Columbus used only the egg.
When the nobleman gave up Columbus simply took the egg and tapped it gently breaking the top of the shell, making it flatter. The moral of the story is normally anyone can solve a problem once they have seen a solution. However, for us, the story shows how to make unstable points stable.
What is more amazing is that you can actually rigorously construct a mathematical algorithm that does exactly this flattening operation. Thus, if a uniform density weeble does exist then following this algorithm will allow us to construct a solid with any number of stable equilbria.
In two weeks we return to the trail of finding this illusive shape.