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Analytic study on construction education based on Euclid’s {\it On divisions}. (Korean. English summary)
East Asian Math. J. 32, No. 4, 483-500 (2016).
Summary: The ancient Greek mathematician Euclid left three books about mathematics. They are {\it Elements}, {\it The data}, and {\it On divisions of figures}. This study is based on the analysis of Euclid’s {\it On divisions of figures}. {\it On divisions of figures} is a book about the construction of the shape. Because, there are thirty six propositions in {\it On divisions of figures}, among them 30 propositions on constructions. In this study, based on the {\it On divisions of figures}, we explore the direction for construction education. The results were as follows. First, the proposition of {\it On divisions of figures} shall include the following information. It is a ‘proposition presented’, ‘heuristic approach to the construction process’, ‘specifically drawn presentation’, ‘proof process’. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of {\it On divisions of figures} is the {\it Elements}. The {\it Elements} includes 25\% construction propositions. However, the geometric constructions contents in the middle school area is only 3\%. Therefore, it is necessary to expand the learning of constructions in the mathematics curriculum.
Classification: G40 G80 D30 A30