2012年美国国际大学生数学建模竞赛(MCM+ICM)题目+翻译.doc

IMPORTANTCHANGETOCONTESTRULESFORMCM/ICM2012:Teams(StudentorAdvisor)arenowrequiredtosubmitanelectroniccopy(summarysheetandsolution)oftheirsolutionpaperbyemailtoHYPERLINK"mailto:".YouremailMUSTbereceivedatCOMAPbythesubmissiondeadlineof8:00PMEST,February13,2012.TeamsarefreetochoosebetweenMCMProblemA,MCMProblemBorICMProblemC.COMAPMirrorSite:Formorein:HYPERLINK""\l"mcm#mcm"MCM:TheMathematicalContestinModelingHYPERLINK""\l"icm#icm"ICM:TheHYPERLINK""\l"icm#icm"InterdisciplinaryContestinModeling2012ContestProblemsMCMPROBLEMSPROBLEMA:TheLeavesofaTree"Howmuchdotheleavesonatreeweigh?"Howmightoneestimatetheactualweightoftheleaves(orforthatmatteranyotherpartsofthetree)?Howmightoneclassifyleaves?Buildamathematicalmodeltodescribeandclassifyleaves.Considerandanswerthefollowing:•Whydoleaveshavethevariousshapesthattheyhave?•Dotheshapes“minimize”overlappingindividualshadowsthatarecast,soastomaximizeexposure?Doesthedistributionofleaveswithinthe“volume”ofthetreeanditsbrancheseffecttheshape?•Speakingofprofiles,isleafshape(generalcharacteristics)relatedtotreeprostructure?•Howwouldyouestimatetheleafmassofatree?Isthereacorrelationbetweentheleafmassandthesizecharacteristicsofthetree(height,mass,volumedefinedbytheprofile)?Inadditiontoyouronepagesummarysheetprepareaonepagelettertoaneditorofascientificjournaloutliningyourkeyfindings.2012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？”怎么能估计树的叶子（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？•你将如何估计一棵树的叶子质量？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？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。PROBLEMB:CampingalongtheBigLongRiverVisitorstotheBigLongRiver(225miles)canenjoyscenicviewsandexcitingwhitewaterrapids.Theriverisinaccessibletohikers,sotheonlywaytoenjoyitistotakearivertripthatrequiresseveraldaysofcamping.RivertripsallstartatFirstLaunchandexittheriveratFinalExit,225milesdownstream.Passengerstakeeitheroar-poweredrubberrafts,whichtravelonaverage4mphorm