Cálculo del área de un polígono simple

Abstract

En el presente trabajo nos planteamos determinar la posición relativa entre un punto y un polígono simple en un plano, para lo cual nos creamos un modelo del polígono, cuya manipulación nos lleva, de una manera muy natural, a la solución de dicho problema y a plantearnos un problema más ambicioso, basado en el mismo modelo: la determinación delárea del polígono. Este ejemplo geométrico esútil para ilustrar el proceso de creación en matemáticas. Se considera de especial interés la manera en la que la formalización de un problema sencillo, con una notación afortunada, y con grandes dosis de exploración algebraica, llevan a redescubrir un interesante resultado geométrico, de mucho mayor alcance que el objetivo inicial.In the present paper we consider to determine the relative position between a point and a simple polygon in a plane. For this purpose we build a model of the polygon, which manipulation carries us, in a very natural way, to the solution of this problem and it allows us to arise a more ambitious problem based on the same model: the determination of the polygon area. This geometric example is useful to illustrate the creation process in Mathematics. It is especially interesting the way in which the formalization of a simple problem with a successful notation and a great dose of algebraic exploration results in a rediscovery of an interesting geometric result which is much more important than the original objective.

Net Assimilation Rate and Agronomic Efficiency of Nitrogen in Tartago (Ricinus communis L.) (Euphorbiaceae) in Dry Climate

“…The net assimilation rate was determined by where NAR is the net assimilation rate, W 2 and W 1 are the dry biomass weights of the plant at the respective time T 2 and T 1 , and LA 2 and LA 1 are the respective leaf areas corresponding to the time T 2 and T 1 [ 7 ]. The leaf area was determined by triangulation of the leaf, dividing the whole leaf in triangles and, later, adding the areas of each leaf to obtain the total area [ 22 ]. When the response variables were found to be significant, Tukey's multiple comparison test was applied at a significance level of 0.05.…”

Analysis and Assessment through Mechanical Static Compression Tests of Damping Capacity in a Series of Orthosis Plantar Materials Used as Supports

“…As the hysteresis curves are described by closed polygonal lines, the shoelace formula was used to calculate the inside area (the generalization of the area of a triangle when the Cartesian coordinates of its vertices are known via the use of determinants) [ 14 ]. The aforementioned formula states that if the Cartesian coordinates (x, y) are the vertices of a closed polygon, the area of the enclosed polygon is [ 14 ] …”

“…The objective was to confirm whether there were relationships between the material’s hardness and its absorption capacity. The correlations between hardness and the dissipation area were evaluated using Pearson’s rank correlation coefficients [ 14 ].…”