La forma hexagonal regular de las células de las abejas como solución de algunos problemas de óptimo
Wax compression and honeycomb resistance, and some other hypothesis as well (elimination of empty spaces between cylindrical cells and approximate emulation of bees bodies) drive to the first optimization problem: among all polygons with n ≥ 3 sides circumscribed into a circle with a given radius, d...
| Autor: | |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1996 |
| País: | Costa Rica |
| Recursos: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Idioma: | español |
| OAI Identifier: | oai:portal.ucr.ac.cr:article/48047 |
| Acesso em linha: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/48047 |
| Access Level: | acceso abierto |
| Palavra-chave: | optimization honeycombs isogonal condition optimizaci´on panales de abejas condici´on isogonal |
| Resumo: | Wax compression and honeycomb resistance, and some other hypothesis as well (elimination of empty spaces between cylindrical cells and approximate emulation of bees bodies) drive to the first optimization problem: among all polygons with n ≥ 3 sides circumscribed into a circle with a given radius, determine the polygon P ∗ n with the smallest perimeter. This extrema problem with an isogonal condition is solved with a Lagrange multipliers method. It is proven that P ∗ n is a regular polygon and n ∈ {3, 4, 6}. Finally, another minimum problem drives to n = 6. |
|---|