Research and Implementation of the Generation Method of Point Array Based on Loop and Iteration

Inhalt:
In Mathematics, a point array refers to a graphic composed of regularly arranged points, for example, numbers in the Pascal’s Triangle are placed in the form of a special point array. By exploring key features of a point array, such as the total number of the points, the arrangement rule of the points, and the relationship between the ordinal number and position of each point, students can improve their observation ability and logical thinking skills, especially in a dynamic mathematics environment Specifically, Dynamic Geometry Software, in which elements can be interactively created and manipulated, is a good choice for learning a point array. However, multi-branch iteration, which is a common method for drawing a point array in the Dynamic Geometry Software, has some problems. For instance, the running efficiency is low, many repeated points are generated, and only one point array can be drawn at a time. Hence, a multiloop single branch iteration method is proposed in this paper. On one hand, generation of repeated points is avoided and the running efficiency is improved; and on the other hand, point arrays of various shapes can be easily drawn, due to the adoption of translation and variables. Moreover, the multi-loop single branch iteration method is verified by drawing two common point array cases, i.e., the Pascal’s Triangle and the snailshell-shaped point array, and it turns out that the method is effective and can be applied to a teaching scene.