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 believe no gentleman would like to have his family affairs neglected because his wife was filling her head with crotchets and pothooks, and who, because she understood a few scraps of Latin, valued that more than minding her needle or providing her husband’s dinner.”
—Sarah Fielding (1710–1768)
“The thinking person has the strange characteristic to like to create a fantasy in the place of the unsolved problem, a fantasy that stays with the person even when the problem has been solved and truth made its appearance.”
—Johann Wolfgang Von Goethe (1749–1832)