2012年美国国际大学生数学建模竞赛(MCM ICM)题目 翻译

IMPORTANT CHANGE TO CONTEST RULES FOR MCM/ICM 2012:

Teams (Student or Advisor) are now required to submit an electronic copy (summary sheet and solution) of their solution paper by email to solutions@comap.com. Your email MUST be received at COMAP by the

submission deadline of 8:00 PM EST, February 13, 2012. Teams are free to choose between MCM Problem A, MCM Problem B or ICM Problem C.

COMAP Mirror Site: For more in:

doc.docsou.com MCM: The Mathematical Contest in Modeling ICM: The Interdisciplinary Contest in Modeling

2012 Contest Problems

MCM PROBLEMS

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?

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