Deltoid (original) (raw)

Furthermore, the fact that the length PQ remains constant gives a (partial) answer to the problem of Kakeya: how to turn around a needle (of length 1) in the plane in such a way that it span an area as small as possible?

Here, the area spanned equals , and it was thought for a long that that this area was the smallest possible one. But in 1928, Besicovitch proved that the needle could be turned around while spanning an area as small as wanted. Nonetheless, in his method, the movement of the ends of the needle is realised by successive approximations, and cannot be made analytical like the deltoidian motion.

Remark: watch out! the needle slips on the deltoid during its movement!