Article : Volume d’un arbre - Colegiul National Emil Racovita (Cluj - Roumanie)

The aim of the paper is the calculation of the volume and of the density of an idealized tree. Every branch in the tree has the form of a truncated cone and is assumed to generate two new smaller branches similar to it. The full tree is obtained by repeating the duplication process infinitely many times on each branch.
The volume of the full tree turns out to be expressed by a geometric series, which is convergent for suitable values of the ratio of similarity between two consecutive branches.
Another result presented in the work regards the density ρ of a tree. It is shown that ρ can be expressed in terms of the density of the dry tree, of the density of water, and of the percentage of water in the wet tree.
An Android application for calculating the volume is presented in the final section.