The Kakeya needle problem asks whether there is a minimum area of a region D in the plane, in which a needle of unit length can be turned through 360°. This question was first posed, for convex regions, by Soichi Kakeya (1917).
He seems to have suggested that D of minimum area, without the convexity restriction, would be a three-pointed deltoid shape. The original problem was solved by Pál. The early history of this question has been subject to some discussion, though.
Read more about this topic: Kakeya Set
Famous quotes containing the words needle and/or problem:
“Up through the lubber crust of Wales
I rocketed to astonish
The flashing needle rock of squatters,
The criers of Shabby and Shorten,
The famous stitch droppers.”
—Dylan Thomas (1914–1953)
“Every child is an artist. The problem is how to remain an artist once he grows up.”
—Pablo Picasso (1881–1973)