Minimization of the sum of squares of distances to vertices in convex polygons
The minimization of the sum of squares of the distances between a point P and the vertices of a convex polygon, weighted by non-negative constants is discussed in this article. Initially, the minimization process is applied to non-degenerated triangles, and then a discrete set of points forming a co...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Institución: | Universidade Estadual do Sudoeste da Bahia (UESB) |
| Repositorio: | Revista Intermaths |
| Idioma: | portugués |
| OAI Identifier: | oai:ojs.pkp.sfu.ca:article/11309 |
| Acceso en línea: | https://periodicos2.uesb.br/intermaths/article/view/11309 |
| Access Level: | acceso abierto |
| Palabra clave: | Center of Mass Centroid Baricenter Two variable functions Centro de massa Centroide Baricentro Funções de duas variáveis |
| Sumario: | The minimization of the sum of squares of the distances between a point P and the vertices of a convex polygon, weighted by non-negative constants is discussed in this article. Initially, the minimization process is applied to non-degenerated triangles, and then a discrete set of points forming a convex polygon is analyzed. In both cases, the analytical results, using Differential Calculus, are presented in detail together with graphical representations of the respective solutions by means of the software GeoGebra. These, in turn, use dynamic color features and make it possible to visualize and explore geometric results and illustrate the minimum points. |
|---|