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:
“I would build my house of crystal,
With a solitary friend,
Where the cold cracks like a pistol
And the needle stands on end.”
—Robert Frost (1874–1963)
“I don’t have any problem with a reporter or a news person who says the President is uninformed on this issue or that issue. I don’t think any of us would challenge that. I do have a problem with the singular focus on this, as if that’s the only standard by which we ought to judge a president. What we learned in the last administration was how little having an encyclopedic grasp of all the facts has to do with governing.”
—David R. Gergen (b. 1942)