Resumo:

"A flow of point particles falls vertically downward on a square table of size 1m x 1m. It is allowed to put inclined mirrors on the table; the height of each mirror is 1cm at most. The inclination of the reflecting part of each mirror is 45. When a particle hits a mirror, it is reflected elastically and then moves freely in a horizontal direction. The mirrors do not impede the motion of particles; that is, the reflected particles do not meet mirrors anymore. It is required to find a configuration of mirrors that ensures full redirection of the incident flow. We solve this problem and some related problems of Newtonian aerodynamics. The idea of the main part of construction is inspired by Besicovitch’s solution of the Kakeya problem: what is the minimum area of a plane region in which a unit line segment can be rotated continuously through 360."