2012年美赛MCMICM题目以及翻译分析.docx

PROBLEM A: The Leaves ofa 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 ofa 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. 怎样估计叶子的重量?估计书的任意部位的重量?分类树叶?建模描述并分类叶子。思考并回答一下问题: 为什么叶子有他们的不同形状? 叶子是否有重叠“最小”的形状, 以至于整个暴漏面积最大?叶子在树上的位置( 体积、枝干)是否影响形状? 通常,叶子的轮廓与树的轮廓/ 枝干形状有关吗? 怎样估计一棵树的叶子总量? 其是否与树的特性(高、重、体积。。)有关? PROBLEM B: Camping along the Big Long River Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is essible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the re