Still looking for a special present for a special person? Then what about a Gömböc: this strange egg-like shape wriggles around with an apparent will of its own and, even better, barely exists at all.
A Gömböc is a 3D convex shape with one stable and one unstable equilibrium point. The reason it wriggles around when you put it down is that it's "trying to" rest on its stable equilibrium point, and since there's only one of them it takes a little dance to find it. for other objects this doesn't happen because they have more stable equilibrium points, so all they need to do to find one when you put them down in an unstable position is fall over. If you change a Gömböc even only a tiny bit, you'll create extra equilibrium points or stop it from being convex, so you'll stop it from being a Gömböc. This is why Gömböcs teeter on the brink of existence — the smallest change and they're gone.
For a very long time people believed that Gömböcs didn't exist, but recently the Hungarian mathematicians Gábor Domokos and Péter Várkonyi proved that they did (find out more here). You can purchase your very own Gömböc on the Gömböc website (though be warned, it's a little pricey!).
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