• Title/Summary/Keyword: Eratosthenes

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

• Oh, Jun-Young
• Journal of the Korean Society of Earth Science Education
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• v.10 no.2
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• pp.214-225
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• 2017
• 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.

### Performance Enhancement of Parallel Prime Sieving with Hybrid Programming and Pipeline Scheduling (혼합형 병렬처리 및 파이프라이닝을 활용한 소수 연산 알고리즘)

• Ryu, Seung-yo;Kim, Dongseung
• KIPS Transactions on Computer and Communication Systems
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• v.4 no.10
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• pp.337-342
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• 2015
• We develop a new parallelization method for Sieve of Eratosthenes algorithm, which enhances both computation speed and energy efficiency. A pipeline scheduling is included for better load balancing after proper workload partitioning. They run on multicore CPUs with hybrid parallel programming model which uses both message passing and multithreading computation. Experimental results performed on both small scale clusters and a PC with a mobile processor show significant improvement in execution time and energy consumptions.

### Performance Enhancement of Parallel Prime Sieving Computation with Hybrid Programming and Pipeline Scheduling (하이브리드 프로그래밍과 파이프라인 작업을 통한 병렬 소수 연산 성능 향상)

• Ryu, Seung-yo;Kim, Dongseung
• Proceedings of the Korea Information Processing Society Conference
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• 2015.04a
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• pp.114-117
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• 2015
• 이 논문에서는 소수 추출 방법인 Sieve of Eratosthenes 알고리즘을 병렬화하되 실행시간과 에너지 소모 면에서 개선된 효과를 얻고자 한다. 멀티코어 프로세서의 공유 메모리를 효율적으로 활용하도록 하이브리드 병렬 프로그래밍 모델을 적용하고, 부하 균등화를 정교하게 조절하도록 파이프라인 작업 방식을 도입하였다. 실험결과 이전 방식보다 연산속도가 향상되었고, 에너지 사용량도 감소함을 확인하였다.

### 부정방정식에 대하여

• 최상기
• Journal for History of Mathematics
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• v.16 no.1
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• pp.17-24
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• 2003
• The Pythagorean equation $x^2{＋}y^2{=}z^2$ and Pythagorean triple had appeared in the Babylonian clay tablet made between 1900 and 1600 B. C. Another quadratic equation called Pell equation was implicit in an Archimedes' letter to Eratosthenes, so called ‘cattle problem’. Though elliptic equation were contained in Diophantos’ Arithmetica, a substantial progress for the solution of cubic equations was made by Bachet only in 1621 when he found infinitely many rational solutions of the equation $y^2{=}x^3{-}2$. The equation $y^2{=}x^3{+}c$ is the simplest of all elliptic equations, even of all Diophantine equations degree greater than 2. It is due to Bachet, Dirichlet, Lebesque and Mordell that the equation in better understood.

### Teachers' & Students' Concepts of the Measurement of the Size of the Earth

• Chae, Donghyun;Han, Jejun
• Journal of The Korean Association For Science Education
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• v.33 no.3
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• pp.639-649
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• 2013
• The purpose of this study is to figure out how teachers conduct an experiment in measuring the size of the Earth and how students recognize it. For this study, an in-depth interview was conducted one week after the lesson on the experiment about measuring the size of the Earth. The participants were five secondary school teachers and five secondary school students. The in-depth interview was recorded and transcribed. The result of the interview was drawn through an inductive categorized analysis method. As a conclusion of this study, the teachers taught the students the lesson using alternate angles instead of using the altitude of the Sun. Their lessons were based on Eratosthene's story or some related illustrations suggested in the textbook and not based on an explanation of the principle. Also, students measured the Earth's size only by using alternate angles and didn't understand the meaning of the shadow in the experiment. The results of this study show that teachers need to reconstruct the textbook and understand the accurate experimental principle for the students to have a meaningful experience of the experiment on measuring the size of the Earth.

### Analysis of Experiments for 'Measuring the size of Earth in 8th Science Textbooks

• Chae, Dong-Hyun
• Journal of The Korean Association For Science Education
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• v.30 no.7
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• pp.901-907
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• 2010
• The purpose of this study is to analyze methods for measuring the size of the Earth, put forth in 6 different Korean 8th grade science textbooks. The research questions are as follows: 1) Do they adequately map out the experiments for measuring the size of the earth by using the concept of the sun's altitude? 2) Do they reduce the size of the sun like as the Earth is similarly downsized to the globe? 3) Do they suggest the precise experimental conditions for selecting two equal longitudinal spots for measuring the size of the earth? 4) Do they design adequate experiments for exact measurement? 5) Do they offer a proportional expression for seeking the size of globe which is easily understood by students? 6) Do they develop experiments to measure actual size of the earth? Four graduate students and one researcher took part in this study. All conditions were unanimously agreed upon by the participants. The results are as follows. First, one publishing company must include the concept of the sun's altitude to accurately measure the size of the Earth. However, some textbooks fail to mention this. As such, the concept of the sun's altitude must be introduced to accurately measure the size of the Earth. Second, a reduced size globe is used as the actual earth so; the sun should be factored in with a reduced light value. Third, you have to lay a stress on two points at the same longitude. In other words, a shadow located at the same longitude from two randomly selected points. Most textbooks mention two points at the same longitude but two of them design the experiment with a shadow at the same longitude. Fourth, we need a method to precisely measure the angle between a stick and its shadow. The angle between the stick and the tip of its shadow is the sun's altitude difference. Fifth, we need to present more specific proportional expressions for calculating the size of the globe. Only 3 out of the 6 texts employed a proportional expression. Sixth, we need to calculate the size of the earth by accurately presenting the scale of the globe to attain the goal of the experiment. Two of the texts analyzed, designed the experiment for the purpose of calculating the size of the globe. Three of the texts designed their experiments to calculate the radius of globe which is not even relevant to the purpose of experiment.

### A Case Study of Service Education Activities Applying Mathematics into a Place-Based Earth Science Program: Measuring the Earth's Size (수학과 연계한 장소기반 지구과학 프로그램에 대한 교육봉사활동 사례 연구: 지구의 크기 측정)

• Yu, Eun-Jeong;Kim, Kyung Hwa
• Journal of the Korean earth science society
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• v.40 no.5
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• pp.518-537
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• 2019
• This study examined the implications of a place-based earth science program integrated with Mathematics. 11 pre-service earth science teachers and 22 middle school students participated in the service education activities of earth science for 30 hours focusing on the measurement of the earth's size through earth science experiments as part of the middle school curriculum. In order to minimize errors that may occur during the earth's size measurement experiments using Eratosthenes's shadows length method of the ancient Greek era, the actual data were collected after triangulation ratios were conducted in the locations of two middle schools: one in remote metropolitan and the other in rural area. The two schools' students shared the final estimate result. Through this process, they learned the mathematical method to express the actual data effectively. Participants, experienced the importance and difficulty of the repetitive and accurate data acquisition process, and also discussed the causes of errors included in the final results. It implies that a Place-Based Earth Science Program activity can contribute to students' increased-understanding of the characteristics of earth science inquiry and to developing their problem solving skills, thinking ability, and communication skills as well, which are commonly emphasized in science and mathematics in the 2015 reunion curriculum. It is expected that a place-based science program can provide a foundation for developing an integrated curriculum of mathematics and science.