# 2012MCM.pdf

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MCM 20112 赛题 赛前精心准备必选
Team#12755 Page 3 of 18 Introduction Team#12755 Page 4 of 18 Properties of Good Model Research about the shape of leaves Background Team#12755 Page 5 of 18 oval lanceolate obovate elliptical spatulate cordate oblanceolate obcordate oblong linear peltate cuneate reniform Method to describe different shapes Team#12755 Page 6 of 18 Leaves of a Sketching the Fitting the contours I I with mathematic contours tree tools the Classification O fun leaves functions outlines Symbol table Cn CIl R R Team#12755 Page 7 of 18 Details of the models Model 1: ideal-Leaves model Assumption Calculation of leaves is the primary factor affecting leaves' quality for it affects the leaves'surface. Therefore, we consider the shape as a variable. Shape of leaves surface. As far as we can concern. the total number of leaves in one tree cant be accurate counted, however, according to common sense it is easy to tell Team#12755 Page 8 of 18 out the relationship between the leaves weight and surface area 30 25 20 15 0.0287x 5 0 100 200 300 400 500 E00 7 800 Leaf surface (cm2) m=f(s=k s n=gc g M f(sg( Team#12755 Page 9 of 18 S兀·观 b M=f(r:a·b)g(c)=0.0287×兀·a·b·c·n M=0.0287××8×5×135×85=41364.2 Model 2: Shape-Changed Leaves model Calculation (. Kiss, M. Kondrak), we can get that genotype of poplar Team#12755 Page 10 of 18 eaf type n 0 F8Y 10〔 0 5 1% 0 0 0 100 80% 单④4 40% 2 Diploid 0% Aneuploid ■ Tetra|o|d 1 Diploid ■ Anello|d ■ Herluin leaves'shape as shape 2 and 3 instead of oval in ype 2 type 3

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