Browse > Article
http://dx.doi.org/10.14477/jhm.2019.32.3.109

An Analysis on the Naturalness of Natural Logarithm and its Educational Implication  

Park, Sun-Yong (Dept. of Math. Edu., Yeungnam Univ.)
Publication Information
Journal for History of Mathematics / v.32, no.3, 2019 , pp. 109-134 More about this Journal
Abstract
In order to improve the educational situation in which the natural number e and the natural logarithm are dealt with somewhat perfunctorily, this study explores the genetic process in which the natural logarithm and its base e occurred, and has an educational discussion based on that analysed process. Specifically, the study inquires into how the natural logarithm happened in relation to the quadrature of the hyperbolic curves through analysis and thought experimentation in mathematics history. Particularly, it sheds light on the role of e and the naturalness of the natural logarithm in terms of the introduction of the real number exponent. Also, this study discusses what the findings suggest educationally.
Keywords
base; natural logarithm; naturalness; real number exponent;
Citations & Related Records
연도 인용수 순위
  • Reference
1 U. BOTTAZZINI, The Higher Calculus : A History of Real and Complex Analysis From Euler to Weierstrass, New York, Springer-Verlag, 1986.
2 C. B. BOYER, A History of Mathematics, Wiley, 1991. 양영오, 조윤동 역, 수학의 역사(상, 하), 경문사, 2000.
3 R. P. BURN, Alphonse Antonio de Sarasa and Logarithms, Historia Mathematica 28 (2001), 1-17.   DOI
4 J. L. COOLIDGE, The Mathematics of Great Amateurs, London, Oxford University, 1950.
5 J. DHOMBRES, Is One Proof Enough? Travels with a Mathematician of the Baroque Period, Educational Studies in Mathematics 24 (1993), 401-419.   DOI
6 J. FAUVEL, J. GRAY, The History of Mathematics : A Reader, Basingstoke, Macmillan, 1987.
7 A. GARDINER, Infinite Processes - Background to Analysis, New York, Springer-Verlag, 1982.
8 E. A. GONZALEZ-VELASCO, Journey through Mathematics, New York, Springer, 2010.
9 I. GRATTAN-GUINNESS, The Development of the Foundations of Mathematical Analysis From Euler to Riemann, Cambridge, MIT Press, 1970.
10 I. GRATTAN-GUINNESS(ed.), From the Calculus to Set Theory, London, Duckworth, 1980.
11 H. V. LOOY, A Chronology and Historical Analysis of the Mathematical Manuscripts of Gregorius A Sancto Vincentio(1584-1667), Historia Mathematica 11 (1984), 57-75.   DOI
12 L. MAOR, The Story of a Number, NJ, Princeton University Press, 1994. 허민 역, 오일러가 사랑한 수 , 서울, 경문사, 2000.
13 D. E. SMITH, A Source Book of Mathematics, New York, McGraw Hill Book Company, 1929.
14 O. TOEPLITZ, The Calculus : A Genetic Approach, The University of Chicago Press, 1963. 우정호, 임재훈, 박경미, 이경화 역, 퇴플리츠의 미적분학, 경문사, 2006.
15 D. T. WHITESIDE, Patterns of Mathematical Thought in the Seventeenth Century, Archive for History of Exact Sciences 1 (1961), 179-388.   DOI