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http://dx.doi.org/10.30807/ksms.2021.24.2.001

In Newton's proof of the inverse square law, geometric limit analysis and Educational discussion  

Kang, Jeong Gi (Jinyeong Middle School)
Publication Information
Journal of the Korean School Mathematics Society / v.24, no.2, 2021 , pp. 173-190 More about this Journal
Abstract
This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.
Keywords
Newton's ; Inverse Square Law; Parabolic Approximation; Polygon Approximation; Limits of Ratio of Line Segments; Geometric Limits;
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