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...

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Detalles Bibliográficos
Autores: Martins dos Santos, João Paulo, Lima, Marcus Vinícius de Araújo, de Jesus, Alessandro Firmiano, Linares, Juan López
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
Descripción
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.