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:
“Think how stood the white pine tree on the shore of the Chesuncook, its branches soughing with the four winds, and every individual needle trembling in the sunlight,—think how it stands with it now,—sold, perchance, to the New England Friction-Match Company!”
—Henry David Thoreau (1817–1862)
“A serious problem in America is the gap between academe and the mass media, which is our culture. Professors of humanities, with all their leftist fantasies, have little direct knowledge of American life and no impact whatever on public policy.”
—Camille Paglia (b. 1947)