한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
권호 표지

서양의 역사적인 지도제작법의 발달 과정과 수학적 지식의 상호 영향 관계를 통해 본 직교좌표계

A study on the rectangular coordinate system via comparing the interrelated influence between mathematical knowledge evolution and historical development of Cartography in Europe

  • Lee, Dong Won (Department of Mathematics, Teachers College, Kyungpook National University)
  • 투고 : 2012.08.02
  • 심사 : 2012.10.17
  • 발행 : 2012.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

역사적인 지도제작법에 나타난 좌표계와 수학적 직교좌표계의 발전 과정을 비교하면서 위치를 표시하는 직교좌표계는 수학의 해석기하학과는 상관없이 인간 본연에 내재되어 있었던 공간지각능력의 일환으로 발전되어 왔음을 주장한다. 지도제작법의 발전이 해석기하학의 발명 전후 삼각함수, 로그, 기하학, 미적분학, 통계학 등 수학의 여러 분야와 상호 영향을 미치지만 원점의 표시나 음수 좌표의 사용과 같은 수학적 직교좌표계 자체에 대한 발전은 데카르트의 논문 발표 후 100여년 이상 지난 후에 이루어지는 점, 해석기하학을 발명하는데 공헌한 대부분의 수학자들이 당대의 문제 해결에 집중하면서 직교좌표계에 대한 수학적 설명없이 자연스럽게 사용하였던 점을 바탕으로 이런 결론을 얻는다.

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

키워드

참고문헌

  1. J. L. Berggren and A. Jones, Ptolemy's Geography: An Annotated Translation of the Theoretical Chapters, Princeton University Press, 2000.
  2. C. B. Boyer, A History of Mathematics (Second ed.), John Wiley and Sons, Inc., 1991.
  3. F. Cajori, A History of Mathematical Notations, Dover Publications Inc., 1993.
  4. M. Clagett, Oresme Nicole, in Dictionary of Scientific Biography, Vol. X, Ch. C. Gillispie (ed.), New York: Charles Scribner's Sons, 1974.
  5. M. Clagett, Nicole Oresme and the Medieval Geometry of Qualities and Motions, Madison, Wisc, 1968.
  6. R. Cooke, The History of Mathematics: A Brief Course, Wiley Interscience. 1997.
  7. R. Descartes,La geometrie, In Discours de la Methode. Paris: Essellier (Appendix), 1637.
  8. M. Friendly, Milestones in the history of thematic cartography, statistical graphics, and data visualization, Michael Friendly, 2009. http://datavis.ca/milestones/.
  9. R. G. Frisius, Libellus de locorum describendorum ratione, Antwerp, 1533.
  10. M. Jones, Tycho Brahe, Cartography and Landscape in 16th Century Scandinavia, in Hannes Palang (ed), European Rural Landscapes: Persistence and Change in a Globalising Environment, 2004.
  11. M. Maor, Trigonometric Delights, Princeton University Press, 1998.
  12. J. F. Moffitt, Medieval Mappaemundi and Ptolemy's Chorographia,Gesta 32 (1993), pp. 59-68 Published by: International Center of Medieval Art.
  13. J. Napier, Mirifici logarithorum canonis descriptio, 1614. (English translation,A Description of the Admirable Table of Logarithms, published in 1616 by Edward Wright, London: Nicholas Okes).
  14. J. Needham, Science and Civilization in China, Vol.3, Cambridge University Press, 1954.
  15. I. Newton, Enumeration of Lines of the third Order, Generation of Curves by Shadows, Organic Description of Curves, and Construction, of Equations by Curves, 1760.
  16. B. Otto, Linear Algebra with Applications, (3rd Edition ed.) Upper Saddle River NJ: Prentice Hall, 1995.
  17. J. Stillwell, Mathematics and its History (Second Edition ed.). Springer verlag, 2004.
  18. J. R. Stone, The Medieval Mappaemundi: Toward an Archaeology of Sacred Cartography, Religion 23(3) (1993), pp. 197-216. https://doi.org/10.1006/reli.1993.1019
  19. P. D. Thomas,Conformal Projections in Geodesy and Cartography, United States Government Printing Office, Washington, Special Publication No. 251, 1952.
  20. L. da Vinci, Notebooks vol.M, Verso 40. Paris: Manuscripts of the Institute of France. 1500.
  21. B. A. Rosenfeld, A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, Springer, 1988.
  22. http://www.henry-davis.com/MAPS/AncientWebPages/AncientL.html, Mesopotamian City Plan, Nippur 1500 BC, 101.
  23. http://www.henry-davis.com/MAPS/AncientWebPages/AncientL.html, World map according to Eratosthenes (194 B.C.), 112.
  24. http://en.wikipedia.org/wiki/Marinus_of_Tyre.
  25. http://www.henry-davis.com/MAPS/EMwebpages/EML.html, 226A Hereford mappa-mundi, Richard de Bello of Haldingham, 1290, color redrawing.
  26. http://www.henry-davis.com/MAPS/AncientWebPages/119.html, 119 Ptolemaic World Map, 12th-13th century.
  27. http://www.henry-davis.com/MAPS/EMwebpages/EML.html, 201F Macrobian world map, 9 th century.
  28. http://www.henry-davis.com/MAPS/EMwebpages/EML.html, 205Z T-O map, unknown, from 12th century edition of Bede's De natura rerum (8.1 cm diameter).
  29. http://en.wikipedia.org/wiki/Mercator_1569_world_map, The 1569 Mercator map of the world.