# Packing Squares with Side 1/n

Packing Squares with Side 1/n

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 , ,, …, . What is the smallest rectangle that can contain the squares as ? One bound is =-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 × was enough. The current record is held by Marc Paulhus, who developed the packing algorithm used for this Demonstration.

1

2

1

3

1

4

1

n

n∞

∞

∑

n=2

1

2

n

2

π

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5

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