Mathematical Model for the Tree Leaf Shape and Estimation of Leaf Mass

Yang Liu; Zhao Liu; Yu Zhang; Qian Yao Duan

doi:10.4028/www.scientific.net/AMR.557-559.2015

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 557-559Mathematical Model for the Tree Leaf Shape and...

Mathematical Model for the Tree Leaf Shape and Estimation of Leaf Mass

Abstract:

The relationship between leaf shape and tree profile is discussed in this paper at first. Through analysis of Leonardo’s rule, Fibonacci sequence and growth regulation, we conclude that leaf shape is related to sunlight, tree profile, and the distribution of leaves. Then by constructing an integral equation of the leaf-mass density, a mathematical model is established to estimate leaf mass of a tree when the density nearly obeys gamma distribution. At last, some numerical experiments are presented to confirm the proposed model.