id: 06617821
dt: j
an: 2016e.00969
au: Pollak, Henry
ti: Raking leaves.
so: Consortium 110, 3-5 (2016).
py: 2016
pu: COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
la: EN
cc: M90 I40
ut: mathematical model building; line segments; intervals; mathematical
applications; minimization of work; optimization; $n$ piles;
differential calculus; continuous model; discretization
ci:
li:
ab: From the text: In the fall, raking leaves is a major chore in many
households. Leaves must be gotten off the ground and, typically, into
one pile. In the olden days, after a decent interval for jumping, the
pile was then burnt; nowadays, it is more likely to be the compost
pile, or the place from where the leaves will be taken to the dump. How
do the leaves get to this terminal location? Usually the leaves will be
raked into a number of smaller piles, and then carried in baskets, old
sheets, or bags to the designated spot. Sometimes they are blown rather
than raked, but raking is the more strenuous activity, and will be
assumed in our model. The question we wish to address concerns these
intermediate piles. How many are there, how big are they, how far apart
are they, and which leaves go into which pile? Observation confirms
that the piles are neither too big nor too small: If the total amount
of leaves is significant, we do not rake them all into ONE pile. On the
other hand, if we considered each leaf a separate pile and carried it
individually to the designated spot, the casual observer and, more
importantly, the spouse, would probably accuse us of malingering. There
seems to be an intuitive optimum: Somehow, we know how many piles to
make, and where to put them. When the raking gets to be too strenuous,
we seem to stop moving that particular mass of leaves and start on a
new pile.
rv: