PROBLEM A: The Leaves of a Tree 树上的树叶
“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:
“一棵树上的树叶总共有多重？”我们怎么估计一棵树上树叶的实际重量（）？怎么把树叶归类？建立一个数学模型用于描述和归类树叶。思考并回答下列问题：
• Why do leaves have the various shapes that they have? 为什么树叶有各种各样的形状？
• 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?
树叶的形状会不会是把投射到其它树叶上的影子最小化的结果，这样就可以让整棵树进行光合作用的面积最大？树叶在整棵树以及树干的“空间”分布会影响到树叶的形状吗？
• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?
考虑轮廓，树叶的形状（的普遍特征）跟树的轮廓以及树枝的构造有关系吗？ • 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)?
你会如何估计一棵树上一片树叶的质量？一片树叶的质量跟树的特征（高度，质量，（用轮廓定义的）体积）有什么关联吗？
In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings. 在你们摘要的基础上，另外准备一页纸内容的书信向一位科技杂志的编辑描述你们的关键发现。
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 inaccessible 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 rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings. 大长河（225公里）的游客可以欣赏优美的景色和令人兴奋的白色水流湍急。这条河是无法徒步观赏的，那么享受它的唯一途径是采取一河之旅，期间需要数天的晚上露营。所有这条河流的旅行都是从头到尾的，从上游到下游总共225英里进行旅行。乘客采取要么使用桨为动力的胶筏，平均4英里，要么使用机动船，平均8英里每小时平均旅行旅行。旅行从开始到结束需要在河边露营的6至18晚。政府机构，希望每位游客都能在这条河享受旷野的经验，以及与河上其他旅客的船进行最少的接触。目前，X支旅行队伍在一年的六个月范围内，前往大长河旅行（在今年余下时间，实在是太寒冷）。有Y个营地相当均匀地分布在整个河岸上。鉴于漂流在河的知名度上升，公园管理人员已被要求让更多人次前往顺流而下。他们希望以确定它们在时间上（在河上的露营多少个晚上来衡量）和交通工具上（马达或桨）的尽可能最好的混合方式。换句话说，乘船游览大长河的漂流季节可以安排多少旅行队伍？河流旅行经理已经聘请你，向他们就如何制定最好的时间表，并就如何确定河流的承载能力给出建议，记住，没有两队营员可以在同一时间占据同一站点。另外给你一个页面汇总表，准备一个页的备忘录描述你的主要结果的河流的管理者。
上面的翻译大家可以参考一下，不一定完全准确，有模糊的地方一定要跟小组同学互相讨论。
本博客文章如非说明转载，均为原创，转载请注明： 转载自MC·Doing Studio
本文链接地址: 2012 Contest 以及翻译
