DOI QR코드

DOI QR Code

Understanding the Estimation of Circumference of the Earth by of Eratosthenes based on the History of Science, For Earth Science Education

  • Received : 2017.07.28
  • Accepted : 2017.08.25
  • Published : 2017.08.31

Abstract

The first accurate estimate of the Earth's circumference was made by the Hellenism scientist Eratosthenes (276-195 B.C.) in about 240 B.C. The simplicity and elegance of Eratosthenes' measurement of the circumference of the Earth by mathematics abstraction strategies were an excellent example of ancient Greek ingenuity. Eratosthenes's success was a triumph of logic and the scientific method, the method required that he assume that Sun was so far away that its light reached Earth along parallel lines. That assumption, however, should be supported by another set of measurements made by the ancient Hellenism, Aristarchus, namely, a rough measurement of the relative diameters and distances of the Sun and Moon. Eratosthenes formulated the simple proportional formula, by mathematic abstraction strategies based on perfect sphere and a simple mathematical rule as well as in the geometry in this world. The Earth must be a sphere by a logical and empirical argument of Aristotle, based on the Greek word symmetry including harmony and beauty of form. We discuss the justification of these three bold assumptions for mathematical abstraction of Eratosthenes's experiment for calculating the circumference of the Earth, and justifying all three assumptions from historical perspective for mathematics and science education. Also it is important that the simplicity about the measurement of the earth's circumstance at the history of science.

지구크기에 대한 최초의 정확한 측정은 기원전 230년, 헬레니즘의 과학자인, 에라토스테네스 (276-195 B.C.)에 의하여 이루어졌다. 역사적으로 수학적 추상화는 유럽의 고대 그리스인의 천재성을 보여주는 좋은 예이다. 그 당시에는 상상하기 어려운 태양이 멀리 떨어져 있기에 태양광선이 평행하게 지구에 입사한다는 전제를 요구하는, 논리적이고 과학적인 기법의 에라토스테네스의 과학적 방법의 성공이었다. 중요한 것은 간단한 수학적 비례식을 성립하기 위해서는 지구가 둥글고, 광선이 지구에 나란하게 들어온다는 가정이 필요하였다. 즉 천상으로부터 지상으로 유클리드 기학학이 연결된다는 내용이다. 그것은 최초로 태양중심을 주장한 아리스타쿠스의 제안을 받아들여야 했고, 아리스토텔레스의 자연관인 우주는 아름답고 우아하다는 사상에 기반을 두어 지구는 구처럼 대칭적이라는 것이다. 우리는 이러한 가정들을 현대가 아닌 그 당시 어떻게 정당화 했는지를 탐색하는 것이다. 또한 실험의 미적 관점에서 에라토스테네스의 지구측정의 중요한 특징은 단순성에 있다는 것을 강조하는 것이다.

Keywords

Acknowledgement

Supported by : Hanyang University

References

  1. Brown, J. R. (2011). The Laboratory of the Mind: Thought Experiments in the Natural Science. London: Routledge.
  2. Chae, D.-H. (2012). Measuring the Earth's Size Using the Sun's Altitude and The Responses. Journal of the Korean Society of Earth Science Education, 5(1), 88-94.
  3. Collins, R. (1998). The sociology of philosophies: A global theory of intellectual change. Cambridge, MA: Harvard University Press.
  4. Crease, R. P. (2003). The Prism and the Pendulum: The ten most beautiful experiments in science. New York, NY: Random House
  5. Cushing, J. T. (1998). Philosophical Concepts in Physics: The Historical Relation between Philosophy and Scientific Theories. Cambridge: University Press.
  6. Dicks, D. R. (1971). Eratosthenes. Dictionary of Scientific Biography. New York: Charles Scribner's Sons
  7. Evans, J. (1998). The History and Practice of Ancient Astronomy, N.Y., Oxford: Oxford University Press
  8. Fraknoi, A., Morrison, D,. & Wolff, S. (1998). VOYAGES through the universe. Saunders college publishing.
  9. Frank, A. (2011). About Time: Cosmology and Culture at the Twilight of the Big Bang. New York: Free Press, a Division of Simon & Schuster, Inc.
  10. Gulbekian, E. (1987). The origin and value of the stadium unit used by Eratosthenes in the third century B.C. Archive for History of Exact Sciences, 37(4), 359-363. https://doi.org/10.1007/BF00417008
  11. Heath, S. T. L. (1913). Aristarchus of Samos. New York: The Clarendon Press at Oxford University
  12. Hosson, C. D. and Decamp, N. (2014). Using Ancient Chinese and Greek Astronomical Data: A Training Sequence in Elementary Astronomy. Science & Education, 23, 809-827. https://doi.org/10.1007/s11191-013-9625-2
  13. Hoyle, F. (1972). Astronomy, New York: Crescent Books.
  14. Kline, M. (1967). Mathematics for the Nonmathematician. New York: Dover Publications, Inc.
  15. Lloyd, G.E.R. (1970). Early Greek Science: Thales to Aristotle. London: Chatto & Windus.
  16. Layser, D. (1984). Constructing the Universe. New York: Scientific American Library
  17. McClean III, J. E. and Dorn, H. (1999). Science and Technology in World History: An Introduction. Baltimore and London: The Johns Hopkins University Press.
  18. Nisbett, R.E. (2003). The Geography of Thought: How Asian and Westerns Thinker Differently ... and Why. New York: A Division of Simon & Schuster Inc.
  19. Oh, J.-Y. (2016). Understanding Galileo's dynamics through Free Falling Motion. Foundations of Science, 21(4), 567-578. https://doi.org/10.1007/s10699-015-9426-y
  20. Poincare, H. (1946). The foundations of science (Translated by G. Halsted). Lancaster, PA: Science Press.
  21. Siebold. J. (1998). Cartographic Images. 12 Feb. 1998. Henry Davis Consulting Inc. 3 Mar. 2005 .
  22. Toulmin, S. & Goodfield, J. (1961). The Fabric of The Heavens: The development of astronomy and dynamics. Chicago and London: the University of Chicago Press.
  23. Zee, A. (2007). Fearful Symmetry: The Search for Beauty in Modern Physics. Princeton and Oxford: Princeton University Press.