Madera y bosques
versão impressa ISSN 1405-0471
CRUZ DE LEON, Gildardo. A general sectional volume equation for classical geometries of tree stem. Madera bosques [online]. 2010, vol.16, n.2, pp. 89-94. ISSN 1405-0471.
This work refers to the classical theory of tree stem form. It shows the derivation of a general sectional volume equation for frustums of solids of revolution generated by the function y2= pnxn where, pn is a positive constant, and nany positive integer. The cylinder case presents a singular situation because of its sectional volume equation cannot be defined for n = 0 as it is known for the generating function. However, that geometry is implicit as a trivial solution of the derived equation. The known sectional volume equations for frustums of paraboloid, conoid and neiloid are particular cases of that equation for n =1, 2, and 3, respectively. The general sectional volume equation has an unexpected statistical nature. It is given as an arithmetic mean of geometric means The classical theory of tree stem form continue being present in the forest measurement teaching and research. This work could contribute to improve the understanding on that theory.
Palavras-chave : Dendrometry; applied mathematics.