PackingSquaresWithSide1N-author

说明：  矩形内排样。A finite volume of potatoes will fit in a finite sack. This seemingly simple statement leads to a family of very difficult questions, sometimes called potato sack problems.Consider squares with sides 1/2, 1/3,1/4, \[Ellipsis], 1/n. What is the smallest rectangle that can contain the squares as n-> \[Infinity]? One bound is \!\( \*UnderoverscriptBox[\(\[Sum]\), \(n = 2\), \(\[Infinity]\)] \*FractionBox[\(1\), SuperscriptBox[\(n\), \(2\)]]\)=\[Pi]^2/6-1, but no one has found a packing for a rectangle of that area. In 1968, Meir and Moser showed that a square of size 5/6*5/6 was enough. The current record is held by Marc Paulhus, who developed the packing algorithm used for
(A finite volume of potatoes will fit in a finite sack. This seemingly simple statement leads to a family of very difficult questions, sometimes called potato sack problems.)