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PROBLEM A: The Leaves of a Tree
"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:
• Why do leaves have the various shapes that they have?
• Do the shapes ¡°minimize¡± overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the ¡°volume¡± of the tree and its branches effect the shape?
• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?
• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?
In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.
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