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:
“The meteor that thrusts in with needle bill,
And off a blossom in mid-air stands still.”
—Robert Frost (1874–1963)
“The writer operates at a peculiar crossroads where time and place and eternity somehow meet. His problem is to find that location.”
—Flannery O’Connor (1925–1964)