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phly鐵桿木蟲 (小有名氣)
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[求助]
數(shù)學(xué)建模A題“一棵樹的葉子有多重？”，求思路，求集思廣益。
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各位大蝦，小蟲這次數(shù)學(xué)建模美賽選做A題，但思路和專業(yè)背景不甚明了，現(xiàn)將題目粘貼如下，敬請各位大蝦不吝賜教，多謝了 中文翻譯： “一棵樹的葉子有多重？”怎么能估計樹的葉子（或者樹的任何其它部分）的實際重量？怎樣對葉子進行分類？建立一個數(shù)學(xué)模型來對葉子進行描述和分類。模型要考慮和回答下面的問題： • 為什么葉子具有各種形狀？ • 葉子之間是要將相互重疊的部分最小化，以便可以最大限度的接觸到陽光嗎？樹葉的分布以及樹干和枝杈的體積影響葉子的形狀嗎？ • 就輪廓來講，葉形（一般特征）是和樹的輪廓以及分枝結(jié)構(gòu)有關(guān)嗎？ • 你將如何估計一棵樹的葉子質(zhì)量？葉子的質(zhì)量和樹的尺寸特征（包括和外形輪廓有關(guān)的高度、質(zhì)量、體積）有聯(lián)系嗎？ 除了你的一頁摘要以外，給科學(xué)雜志的編輯寫一封信，闡述你的主要發(fā)現(xiàn)。 英文原文： 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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