A general sectional volume equation for classical geometries of tree stem
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 n any positive integer. The cylinder case presents a singular situ...
| Main Author: | |
|---|---|
| Format: | Online |
| Language: | eng |
| Published: |
Instituto de Ecología, A.C.
2016
|
| Online Access: | https://myb.ojs.inecol.mx/index.php/myb/article/view/1174 |
| _version_ | 1799769219390242816 |
|---|---|
| author | Cruz de León, Gildardo |
| author_facet | Cruz de León, Gildardo |
| author_sort | Cruz de León, Gildardo |
| collection | MYB |
| description | 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 n any 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. |
| format | Online |
| id | oai:oai.myb.ojs.inecol.mx:article-1174 |
| institution | Madera y Bosques |
| language | eng |
| publishDate | 2016 |
| publisher | Instituto de Ecología, A.C. |
| record_format | ojs |
| spelling | oai:oai.myb.ojs.inecol.mx:article-11742022-11-30T00:20:54Z A general sectional volume equation for classical geometries of tree stem Una ecuación general para el volumen de la sección de las geometrías clásicas del tronco de los árboles Cruz de León, Gildardo Dendrometry applied mathematics Dendrometría matemáticas aplicadas 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 n any 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. Este trabajo se refiere a la teoría clásica de la forma del tronco del árbol. Se muestra la derivación de una ecuación de volumen general de la sección de sólidos de revolución truncados generada por la función y2 = pnxn donde, pn es una constante positiva, y n un entero positivo. El caso del cilindro constituye un caso singular pues su ecuación de volumen de la sección no se puede definir para n = 0 , ya que es conocido por la función generadora. Sin embargo, esa geometría está implícita como una solución trivial de la ecuación derivada. Las ecuaciones conocidas de volumen de secciones truncadas de paraboloides, conoides y neiloides son casos particulares de la ecuación para n = 1, 2 y 3, respectivamente. La ecuación general de volumen de la sección es de una naturaleza estadística inesperada. Se da como una media aritmética de medias geométricas. La teoría clásica de la forma del árbol sigue estando presente en la enseñanza de medición e investigación forestal. Este trabajo podría contribuir a mejorar la comprensión de esa teoría. Instituto de Ecología, A.C. 2016-08-30 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Nota científica evaluada por pares application/pdf https://myb.ojs.inecol.mx/index.php/myb/article/view/1174 10.21829/myb.2010.1621174 Madera y Bosques; Vol. 16 No. 2 (2010): Verano 2010; 89-94 Madera y Bosques; Vol. 16 Núm. 2 (2010): Verano 2010; 89-94 2448-7597 1405-0471 eng https://myb.ojs.inecol.mx/index.php/myb/article/view/1174/1354 Derechos de autor 2016 Madera y Bosques |
| spellingShingle | Cruz de León, Gildardo A general sectional volume equation for classical geometries of tree stem |
| title | A general sectional volume equation for classical geometries of tree stem |
| title_full | A general sectional volume equation for classical geometries of tree stem |
| title_fullStr | A general sectional volume equation for classical geometries of tree stem |
| title_full_unstemmed | A general sectional volume equation for classical geometries of tree stem |
| title_short | A general sectional volume equation for classical geometries of tree stem |
| title_sort | general sectional volume equation for classical geometries of tree stem |
| url | https://myb.ojs.inecol.mx/index.php/myb/article/view/1174 |
| work_keys_str_mv | AT cruzdeleongildardo ageneralsectionalvolumeequationforclassicalgeometriesoftreestem AT cruzdeleongildardo unaecuaciongeneralparaelvolumendelasecciondelasgeometriasclasicasdeltroncodelosarboles AT cruzdeleongildardo generalsectionalvolumeequationforclassicalgeometriesoftreestem |
