Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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An Analysis on the Characteristic and Origin of the Exhaustion Method

실진법의 특성과 기원에 대한 분석

  • Received : 2018.11.13
  • Accepted : 2019.02.25
  • Published : 2019.02.28
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Abstract

This study analyses and discusses on the characteristic and the origin of the exhaustion method caused by the controversy over whether that method succeeded to the Antiphone's complete exhaustion idea and whether that method is similar to the method of limits. First, this study analyses 'principle of exhaustion method' which play an important role in that method in order to grasp the local characteristic of it. And this study speculates the origin of the exhaustion method by considering the time and situation of appearance and looking through the local characteristic of it. Also, this study takes a view of the overall characteristic of the exhaustion method by inquiring into the process of actual application of 'principle of exhaustion method' in a proof. As these results, this study reveals that the exhaustion method uprose not as a succession of Antiphone's idea but as a reaction to its idea, and that the exhaustion method has the recognized character of 'finitude' as distinct from the method of limits.

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References

  1. H. G. APOSTLE, Aristotle's Philosophy of Mathematics, Chicago, The University of Chicago Press, 1952.
  2. C. B. BOYER, The History of the Calculus and Its Conceptual Development, New York, Dover Publications, 1949. 김경화 역, 미적분학사-그 개념의 발달, 서울, 교우사, 2004.
  3. D. M. BRESSOUD, A Radical Approach to Real Analysis(2e), MAA, 1997. 허민 역, 실해석학 (2판)-전혀 새로운 접근-, 교우사, 2009.
  4. T. L. HEATH, The Thirteen Books of Euclid's Elements, New York, Dover Publications, 1956. 이무현 역, 기하학 원론-비율, 수-, 교우사, 1998.
  5. T. L. HEATH, The Thirteen Books of Euclid's Elements, New York, Dover Publications, 1956. 이무현 역, 기하학 원론 -무리수-, 교우사, 1998.
  6. T. L. HEATH, The Works of Archimedes, Cambridge University Press, 2010.
  7. KIM N. H. et al, Mathematics Curriculum and a Study of Teaching Materials, Seoul, Kyung-Moon, 2017.
  8. W. R. KNORR, Infinity and Continuity : The Interaction of Mathematics and Philosophy in Antiquity, In N. Kretzmann(ed.), Infinity and Continuity in Ancient and Medieval Thought, Cornell University Press, 1982.
  9. T. KOUREMENOS, Mathematical Rigor and the Origin of the Exhaustion Method, Centaurus 39(3) (1997), 230-252. https://doi.org/10.1111/j.1600-0498.1997.tb00033.x
  10. I. THOMAS, Greek Mathematics 1, Cambridge, Harvard University, 1967.
  11. O. TOEPLITZ, The Calculus : A Genetic Approach, The University of Chicago Press, 1963. 우정호, 임재훈, 박경미, 이경화 역, 퇴플리츠의 미적분학, 경문사, 2006.