The Korea Society Of Educational Studies In Mathematics

Current Issue

Journal of Educational Research in Mathematics - Vol. 29 , No. 2

[ Article ]
Journal of Educational Research in Mathematics - Vol. 29, No. 1, pp.1-15
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 28 Feb 2019
Received 26 Nov 2018 Reviewed 23 Jan 2019 Accepted 29 Jan 2019
DOI: https://doi.org/10.29275/jerm.2019.2.29.1.1

A Study on the Transition from the Exhaustion Method to the Limit Method of the Early 19th Century
Park, Sun Yong*
*Professor, Yeungnam University, South Korea (polya@yu.ac.kr)

Correspondence to : Professor, Yeungnam University, South Korea, polya@yu.ac.kr

Funding Information ▼

Abstract

In this study, we tried to investigate how the limit method was refined in the early 19th century in relation to the exhaustion method. To achieve this, we assessed the exhaustion method genetical background and compared it to the mathematical situation of the early 19th century. Based on the similarity of two epochs, we discussed Cauchy’s ability to systematize the analysis and refine the limit method. The results of this study indicate that through analyzing the exhaustion method and gaining an insight into the ‘sequence goes near to any value indefinitely’ criterion, Cauchy was able to refine the limit method. The results also suggests that the introduction of the limit method based on the genetic principle is necessary in mathematics teacher education.


Keywords: exhaustion method, limit method, Cauchy

Acknowledgments

이 연구는 2018학년도 영남대학교 학술연구조성비에 의한 것임


References
1. Bledsoe, A. T.(1886). The philosophy of mathematics. Philadelphia: Lippincott Company.
2. Boyer, C. B.(1949). The history of the calculus and its conceptual development. New York : Dover Publications.
3. Bressoud, D. M.(1997). A radical approach to real analysis(2e). Washington: MAA.
4. Grabiner, J. V.(1981). The origins of Cauchy’s rigorous calculus. New York: Dover Publications.
5. Heath, T. L.(1956). The thirteen books of Euclid’s Elements. Cambridge University Press.
6. Heath, T. L.(1998b). 기하학 원론 -비율, 수-. 서울: 교우사.
7. Heath, T. L.(1998c). 기하학 원론(해설서) -공간기하-. 서울: 교우사.
8. Heath, T. L.(2010). The works of Archimedes.. New York: Cambridge University Press.
9. Kim, N. H., Na, G. S., Park, K. M., Lee, K. W., & Jung, Y. O.(2017). Mathematics curriculum and a study of teaching materials. Seoul: KyungMoon.
10. Kim, Y. W.,& Kim, Y. K.(1991). Set theory and mathematics. Seoul: WooSung.
11. Knorr, W. R.(1982). 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.
12. Kouremenos, T.(1997). Mathematical Rigor and the Origin of the Exhaustion Method, Centaurus, 39(3), 230-252.
13. Mancosu, P.(1996). The philosophy of mathematics and mathematical practice in the seventeenth century. New York: Oxford University Press.
14. Toeplitz, O.(1925). Mathematik und Antik, Die Antike(1),, 175-203.
15. Toeplitz, O.(1963). The calculus : a genetic approach. The University of Chicago Press.
16. Weyl, H.(1949). Philosophy of mathematics and natural science,. New Jersey: Princeton University