國中圓的性質之探討

本論文主要針對國中教材圓的性質做探討和研究，而本身是一個國中教師，以多年來的教學經驗及對學生之觀察，用自己的想法加上參考許多版本的教科書南一版(102)、康軒版(102)、適康版(100)和適南版(100)，並且尋找一些由淺入深之練習題來完成本論文，並且也對課外元的理論托勒密定理及其逆定理給予一些證明和反例，並且探討凸多邊形滿足什麼條件會有外接圓和內切圓能夠讓學生在深入的部分得到一些概念，讓他們知道如何去發掘問題並解決，這也是本論文主要目的及貢獻。

關鍵字

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並列摘要

The thesis focalised with the exploration and study on the properties of circular in junior high school level. Based on the teaching experiences and the observation, the researcher, a junior high school teacher, used personal thoughts and refered to the textbooks in different versions, such as Nan-I(102), Kang-hsuan(102), Kang-hsuan fit(100), and Nan-I fit(100) to look for some exercies from basic ones to advanced ones, and to raise some proofs and counterexamples from Ptolemy’s Theorem as well as its converse theorem. In order to let students receive some concepts and know how to find out questions and solutions, the researcher also explored in what conditions, there are circumcircles and inscribed circles in the convex polygons. These are the purposes and contribution from the thesis.