中考路上的“勾股树”与“赵爽弦图”

The “Pythagorean Tree” and “Zhao Shuang’s String Diagram” in the Middle School Entrance Examination

庞加莱说:“如果我们想要预见数学的将来,适当的途径是研究这门科学的历史和现状”。勾股定理的价值是非凡的,它被誉为“几何学的基石”,是欧式几何的基础定理。在日常教学中,以数学文化为入口,学习勾股定理。本文以勾股定理知识为基础,针对其中的“赵爽弦图”和“毕达哥拉斯树”两个知识点为起点,进行题目的对比分析,并给出教学建议。

Henri Poincaré say that if we want to see the future of mathematics, the proper way is to study the history and present state of the science. The value of Pythagorean Theorem is extraordinary, which is called “the cornerstone of geometry”. It’s the fundamental theorem of Euclidean geometry. In the daily teaching, we often learn Pythagorean Theorem with the entrance of mathematical culture. In this paper, by taking the more difficult questions about Pythagorean Theorem in the secondary school entrance examination as an example, we give some teaching advices by using “Zhao Shuang’s string diagram” and “Pythagoras tree” for topic analysis.