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Understanding the Estimation of Circumference of the Earth by of Eratosthenes Based on the History of Science, for Earth Science Education

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Understanding the Estimation of Circumference of the Earth by of Eratosthenes Based on the History of Science, for Earth Science Education Journal of Korean Society of Earth Science Education pISSN: 2005-5668 eISSN: 2289-0386 10(2); 214~225 ; August 2017 https://doi.org/10.15523/JKSESE.2017.10.2.214 ORIGINAL ARTICLE Understanding the Estimation of Circumference of the Earth by of Eratosthenes based on the History of Science, For Earth Science Education Jun-Young Oh (Hanyang University) 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. Key words : Eratosthenes, estimate of the Earth’s circumference, mathematics abstraction, Symmetry, Mathematics & science education, simplicity Ⅰ. INTRODUCTION abstraction had a greater reality (symmetry) than the properties of objects in the physical world (Nisbett, 2003, pp. 156- 157). During the Hellenism period, Greek became the The simplicity and elegance of Eratosthenes’ international language and Greek culture was seen as measurement of the circumference of the Earth by the ideal. One of the most important Hellenism cities mathematics abstraction were an excellent example of was Alexandria in Egypt. It was where Euclid, the ancient Greek ingenuity. Thus, our research should be Greek mathematician, taught geometry and founded a consider Eratosthenes’ activities at that time(Greek school of mathematics. Plato actually thought that philosophy, and Alexandra mathematics), Received 28 July, 2017; Revised 20 August, 2017; Accepted 25 August, 2017 ⓒ The Korean Society of Earth Sciences Education . All rights reserved. *Corresponding author : Jun-Young Oh, Hanyang University, Seongdong-gu, This is an Open-Access article distributed under the terms of the Creative Seoul, 15588, Republic of Korea Commons Attribution Non-Commercial License Phone: +82-10-3665-3791 (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted E-mail: [email protected] non-commercial use, distribution, and reproduction in any medium, provided This work was supported by the 2014 research foundation grant from Hanyang the original work is properly cited. University (H. 201400000001311). Understanding the Estimation of Circumference of the Earth by of Eratosthenes based on the History of Science, For Earth Science Education 215 as both mathematics abstraction involving An acute awareness of the beauty inherent in idealization, and symmetry based on Plato’s thinking, scientific ideas and scientific discovery necessarily geometry based on Euclid, and Aristarchus’s estimate draws us in to its study. between the Sun and the Earth and early Atomism. We remind that “The main recommendations for improving teaching and learning in astronomy and In scientific activity, mathematics abstraction allows physics is that teachers should be encouraged to use the scientists to focus on an object’s particular thought-experiments based on historical examples properties which our mathematics theory deals, while (Eratosthenes’ measurement of the circumference of the deliberately removing (subtract) any other properties Earth), which appeared in all textbooks of South present in the concrete circumstances, by Bold Korea, to stretch students’ imaginations and enhance assumptions. Idealization is the consideration of their reasoning. properties that the object definitely does not possess in Research questions of this study are: 1) to assume actual system, by Idealized assumptions, the notion of specially the Earth’s perfect sphere logically and abstraction, by contrast, deliberately ignores certain empirically, and parallel sun rays at that time, for features the object possesses in concrete circumstances mathematics abstraction based on Greek Philosophy (Oh, 2016) and Alexandria Mathematics, 2) to justify all three It would be wrong to conclude that it was a divine bold assumptions from Greek history, and 3) to search hand that created the Earth as a perfect sphere with a weakness of Eratosthenes’s work (Estimation of religious perfect sphere belief. Symmetry is a powerful Circumference of the Earth) in modern view. tool, and a source of hypotheses that we can make to understand the physical world (Lederman, and Hill, 2004, pp. 18-20). <Axioms>. Given a line l and a point P not on that line, there exists in the plane of a point P and l and through P one and only one line m, which does not meet the given line l (Kline, 1967, p.126) <All three bold assumptions as additional Axioms>: 1. The shape of the Earth is a perfect sphere. 2. The cities of Syene (modern Aswan) and Alexandria are situated on the same longitude. 3. The Sun’s rays that reach the Earth are parallel. Justification of three bold < Geometric Theorems> By Mathematics assumptions through thought abstraction based on three bold assumptions at experiment and real observations at that time that time The results of Measurement of circumference of the Earth Fig 1. Eratosthenes’ Mathematics abstraction strategies based on Euclidian Geometry for the Estimation of Circumference of the Earth 216 Jun-Young Oh Ⅱ. Measurement of circumference of the Earth by Eratosthenes three bold assumptions Ancients’ Chinese historical elements are chosen and organized according to specific educational and conceptual constraints that include the construction of the quasi-parallelism of solar rays reaching Earths’ surface, and the spontaneous modeling of the propagation of Sunlight leaning on divergent rays. Fig 3. Illustration of Eratosthenes’ procedure as described by Diomedes, That was the circular motion of the celestial bodies. Greek philosophy began to spread along with the conquests of Alexander the Great (356-323 B.C.). Alexander the Great entertains great interest in the sciences. This is partially because his private teacher had been Aristotle. Alexander erected a city called Alexandria in Egypt, and the Great Library of Alexandria was established in 300 B.C. This continued as the site of globally leading center for research for Fig 2. According to the Zhou cosmology, every the next 700 years. Eratosthenes (310- 230? B.C.) was displacement on the Earth surface produces a one of several brilliant astronomers to emerge from the length change in the shadow cast by the so-called Alexandrian school, which by his time gnomon (Hosson & Decamp, 2014) already had distinguished tradition. Based on the abstract logic that a perfect sphere and a simple The Chinese text presented hereafter is taken from the mathematical rule exist in reality as in geometry, Chin Shu, a book written around 635 A.D. The Eratosthenes abstracted a simple proportion. The astronomical part of this book has been written by Li Earth’s roundness was already logically and empirically Shun-feˆng. The proposed excerpt refers to the proven by Aristotle (Crease, 2003, p.4). astronomical knowledge under the Zhou dynasty that Eratosthenes’s success was a triumph of logic and began about a thousand year B.C. According to the scientific technique, but it suffered from one Eratosthenes, however, the measurement of the size of weakness. The method required that he assume that the Earth considers two assumptions: the flat surface by Sun was so far away that its light reached Earth along the Chinese and the rays of light parallel to the spherical parallel lines. That assumption, however, was Earth, which in the age of Hellenism, was an audacious supported by another set of measurements made by the assumption, when compared to the Sun that emits lights ancient Greek, namely, a rough measurement of the radially. Therefore, this study aims to investigate, from relative diameters and distances of the Sun and Moon. the literature of Greek philosophers and scientists in As the chief librarian at Alexandria’s city library, you Alexandria rather than that of China, what the origin of can imagine that he read many books. One of those the assumption that the Earth is round was and how it spoke of a well in Syene, Egypt (near Aswan) now was possible to consider that the Sun is far away. – Understanding the Estimation of Circumference of the Earth by of Eratosthenes based on the History of Science, For Earth Science Education 217 known to lie close to the tropic of cancer. He read that <Axiom based on Euclidian Geometry >. Given a every year on the 21st of June at noon, the sun was line l and a point P not on that line, there exists in the positioned so that light rays went straight down the plane of a point P and l and through P one and only well, the sun being directly overhead. This was a one line m, which does not meet the given line l property that never happened in his hometown (Kline, 1967, p.126) Alexandria. This gave him a brilliant idea to calculate He stuck a stick in the ground at Alexandria, the circumference of the earth.
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