2025 美赛 A 题：一棵树的叶子（数学中国翻译）)“一棵树的叶子有多重？”怎么能估量树的叶子（或者树的任何其它部分）的实际重量？怎样对叶子进行分类？建立一个数学模型来对叶子进行描述和分类。模型要考虑和回答下面的问题： • 为什么叶子具有各种形状？ • 叶子之间是要将相互重叠的部分最小化，以便可以最大限度的接触到阳光吗？树叶的分布以及树干和枝杈的体积影响叶子的形状吗？ • 就轮廓来讲，叶形（一般特征）是和树的轮廓以及分枝结构有关吗？ • 你将如何估量一棵树的叶子质量？叶子的质量和树的尺寸特征（包括和外形轮廓有关的高度、质量、体积）有联系吗？ 2 S! V- g9 Y1 d( m) q, Z' W除了你的一页摘要以外，给科学杂志的编辑写一封信，阐述你的主要发现。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 pro 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.2025 美赛 B 题：沿着“大长河”露营【数学中国翻译】 , R) P8 H/ E4 R- ] 游客在“大长河”(225 英里)可以享受到秀丽的风光和令人兴奋的白色湍流。这条河对于背包客来说是进不去的， 因此畅游这条长河的唯一办法...
