FIVE- M IN U T E A N A LYST
Achieving an optimal fill
of the round cup will be
much more difficult than
achieving an optimal fill
of the square box. In fact,
the amount of time that it
takes a child to optimally
fill a box is about the
amount of time that it
takes an adult to create
the bottom level of the
round box.
putting large pieces in first, then filling the rest
of the space with smaller pieces (“elements”),
which for tractability were excluded from this
analysis. The conclusion of this article is that
while they didn’t really look like much, the promotional brickbox was a really nice gift.
As a final note, we observe that achieving
an optimal fill of the round cup will be much
more difficult than achieving an optimal fill of
the square box. In fact, the amount of time that
it takes a child to optimally fill a box is about
the amount of time that it takes an adult to create the bottom level of the round box.
Next time: We answer our original question
of how much better off one is by packing both
the round and square cups than by randomly
tossing bricks in.
Harrison Schramm ([email protected]) is an
operations research professional in the Washington, D.C.,
area. He is a member of INFORMS and a Certified Analytics
Professional (CAP).
NOTES & REFERENCES
1. There is a community of people interested in this problem,
for starters, see Erich’s Packing Center: http://www2.stetson.
edu/~efriedma/squincir/
2. There is a very nice description of the problem at mathworld:
http://mathworld.wolfram.com/GausssCircleProblem.html.
Additionally, Hilbert discusses the problem in “Geometry and
the Imagination,” which I purchased during the course of
writing this article.
3. Sloane’s A000328: 1, 5, 13, 29, 49, 81, 113, 149, 197, 253…
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