摘要
运用几何变换思想,通过构造全等或相似三角形建立“种线得线,种圆得圆”的轨迹映射关系,实现“动态轨迹→静态距离”的转化,运用“瓜豆原理”解决动点最值问题。分析了近年中考动点最值问题,揭示该模型在培养学生几何直观(轨迹预判)、模型思想(关系抽象)、推理能力(变换证明)三个方面的育人价值。将“种瓜得瓜,种豆得豆”的哲学思想引入到几何学习的实际操作中,为落实“三会”核心素养目标提供创新思路。
Using the idea of geometric transformation, the trajectory mapping relationship of “planting lines to get lines, planting circles to get circles” is established by constructing congruent or similar triangles, so as to realize the transformation of “dynamic trajectory → static distance”, and use the “melon bean principle” to solve the problem of the minimum value of the moving point. An analysis of the maximum and minimum problems of moving points in recent Senior High School Entrance Examinations reveals the educational value of this model in three aspects: cultivating students’ geometric intuition (trajectory prediction), model thinking (relationship abstraction), and reasoning ability (transformation proof). The philosophical idea of “planting melons and getting melons, planting beans and getting beans” is introduced into the practical operation of geometric learning, so as to provide innovative ideas for the implementation of the core literacy goals of the “San Hui”.
出处
《应用数学进展》
2025年第7期48-53,共6页
Advances in Applied Mathematics
基金
江汉大学研究生科研创新基金项目(KYCXJJ202350)。
