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http://dx.doi.org/10.7468/jksmee.2022.36.1.23

Understanding the Proof of Inverse Square Law of Newton's Principia from a Heuristic Point of View  

Kang, Jeong Gi (Jinyeong Middle School)
Publication Information
Communications of Mathematical Education / v.36, no.1, 2022 , pp. 23-38 More about this Journal
Abstract
The study provided a perspective on which readers can see Newton's proof heuristically in order to overcome the difficulty of proof showing 'QT2/QR converges to the latus rectum of ellipse' in the proof of the inverse square law of Newton's Principia. The heuristic perspective is as follows: The starting point of the proof is the belief that if we transform the denominators and numerators of QT2/QR into expression with respect to segments related to diameter and conjugate diameter, we may obtain some constant, the desired value, by their relationship PV × VG/QV2 = PC2/CD2 in Apollonius' Conic sections. The heuristic perspective proposed in this study is meaningful because it can help readers understand Newton's proof more easily by presenting the direction of transformation of QT2/QR.
Keywords
principia; inverse square law; heuristic perspective;
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  • Reference
1 Heath, T. L. (1986). Apollonius of perga: Treatise on conic sections. Cambridge: Cambridge University Press.
2 Gandt, F. De (1995). Force and geometry in Newton's principia. New Jersey: Princeton University Press.
3 Guicciardini, Niccolo (1999). Reading the principia. Cambridge: Cambridge University Press.
4 Prentis, J., Fulton, B., Hesse, C., & Mazzino, L. (2007). Elliptical orbit ⇒ 1/r2 force. The physics teacher, 45(1), 20-25.   DOI
5 Sugimoto, T. (2009). How to present the heart of Newton's Principia to the layperson: a primer on the conic sections without apollonius of perga. Symmetry: Culture and Science, 20(1-4), 113-144.
6 Pask, C. (2019). Magnificent principia: exploring Isaac Newton's masterpiece. New York: Prometheus Books.
7 Densmore, D. (2003). Newton's Principia: The central argument, translation, notes and expanded proofs (translation and diagrams by Donahue, W. H.). Santa Fe, New Mexico: Green Lion Press.
8 Brackenridge, J. B. (1995) The key to Newton's dynamics. Berkeley: University of Califonia.
9 Suh, Boeuk (2021). A study on mathematical investigation activity through using one mathematical fact. Communications of Mathematical Education, 35(2), 193-212.   DOI
10 Ogami Masasi, & Wada Smio (2003). Laws of physics solved with mathematics. translated by Lim Jeong (2005). Seoul: Easybook.
11 Fleuriot, J. D., & Paulson, L. (1998). A combination of nonstandard analysis and geometry theorem proving, with application to Newton's principia. Proceedings of the 15 th International Conference on the Automated Deduction, LNAI 1421, 3-16. Springer.
12 Henderson, H. (2005). Of orbits, conics, and grammar. The Physics Teacher, 43(2), 84-87.   DOI