The Leaf Problem

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451

Background Information:

Every fall in the neighborhood in which I live, the crews come by to collect the leaves that have fallen from the neighborhood trees and which are accumulated by lawn services and homeowners along the curb sides of the streets. Sometimes the piles get so large it is hard to find parking because the leaves take up so much room. This season it seemed as if a surprisingly large number of leaves were still on the trees by the end of November.

As I saw the individual beautifully colored leaves floating down I realized there are a variety of interesting mathematical questions one can ask about leaves.

Problem:

a. Pick a specific tree near your home and estimate the weight that the leaves from that tree will contribute to what must be collected by your local sanitation department.

b. Estimate the volume of the leaves that falls from this same tree.

In constructing your model, you will want to consider how to deal with the fact that leaves from the same tree can vary considerably.

Questions to think about:

1. Can one tell different types of trees (pin oak, black oak, maple, tulip) apart by collecting data on the weight of the leaves from these trees?

2. Will the weight of tree leaves differ greatly from when the leaves are fully matured on the trees in the spring to when the leaves fall down from the trees in the fall? If so, why might this be?

3. Younger trees presumably have different numbers of leaves from trees that were planted in the more distant past. Can one somehow use information about the leaves to estimate the age of the tree? Can one use the age of the tree to give more accurate information about the weight of its leaves? How does the weight of the leaves of a very old tree differ from a "middle aged" tree?