• Proceedings of the Korea Society of Mathematical Education Conference
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• 2007.06a
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• pp.21-28
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• 2007

학교수학의 내용 중에는 수학적으로 깊은 의미를 가지고 있지만, 교실수업에서는 자명한 것으로 취급되어 그 중요성이 간과되고 있는 것이 있다. 본 연구에서는 원주율의 값이 상수라는 익숙한 사실을 그 구체적인 예로 들어 수학적 의미를 재음미하는 한편, 아르키메데스가 원주율을 계산한 방법 속에서 교육적 시사점을 찾아 탐구주제로서의 원주율의 가치를 부각시키고자 한다.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.811-831
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• 2017

The purpose of this study is to analyze the contents of pi of Chosun-sanhak and organize the teaching and learning activities to help to understand the concept of pi deeply using the analysis results. The results of this study are as follows. First, Chosun-sanhak used various approximate values of pi and those were represented as the form to reveal the meaning of the ratio of radius and circumference. Second, There were the freedom of selection of the approximate values of pi suitably. Lastly, the enriched leaning about pi need to draw a distinction pi from approximate values of pi, choose the suitable approximate values of pi and compare the method of calculation of circumference and the area of circle of Chosun-sanhak and today's mathematics. In conclusion, I proposed several issues which is worth exploring further in relation to pi and Chosun-Sanhak.

• The Mathematical Education
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• v.47 no.1
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• pp.1-10
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• 2008

Some of school mathematics contents that have deep mathematical meanings are regarded as obvious and their importance is frequently overlooked. We first reexamined the mathematical meaning of pi as a constant. Then we indicated the educational implications of Archimedes' calculation method of pi and finally underlined the availability of pi as a valuable research topic in school mathematics.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.91-110
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• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• Proceedings of the Korea Information Processing Society Conference
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• 2016.04a
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• pp.59-60
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• 2016

본 논문에서는 고성능 병렬 계산 장치로 주목받고 있는 GPU를 CPU와 동시에 병렬로 사용한 계산 성능을 분석하였다. 성능 분석을 위하여 원주율(${\pi}$)을 적분으로 계산하는 CUDA 프로그램을 사용하였으며, 전체 계산을 GPU 대비 CPU 계산 부분으로 할당하여 성능을 분석하였다.

• Proceedings of the Korea Information Processing Society Conference
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• 2016.04a
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• pp.49-50
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• 2016

본 논문에서는 다중 GPU의 효율성을 알아보기 위하여 정적분 계산을 이용하여 원주율(${\pi}$)를 계산하는 CUDA 프로그램을 구현하였으며, 다중 GPU를 사용하기 위해서는 병렬처리 라이브러리인 MPI를 사용하였다. 실험 결과 GPU의 수에 비례하여 성능이 선형으로 증가함을 보였다.

• Journal of KIISE
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• v.42 no.12
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• pp.1467-1473
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• 2015

In this paper, we implemented a parallel random number generation program on GPU's, which are known for high performance computing, using LCG (Linear Congruential Generator). Random numbers are important in all fields requiring the use of randomness, and LCG is one of the most widely used methods for the generation of pseudo-random numbers. We explained the parallel program using the NVIDIA CUDA model and MPI(Message Passing Interface) and showed uniform distribution and performance results. We also used a Monte Carlo algorithm to calculate pi(${\pi}$) comparing the parallel random number generator with cuRAND, which is a CUDA library function, and showed that our program is much more efficient. Finally we compared performance results using multi-GPU's with those of ideal speedups.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.14 no.2
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• pp.119-126
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• 1996

TM projection is widely used for surveying and mapping. However, the complicated computations and process are required and, moreover. the different results of computation may occur according to different formulae and coefficients. In this study, the transformation formulae are classified into 4 categories and the computations are executed according to the categories. The computations are also made to different value of the circular constant, $\pi$. The result of test shows that the enough number of items in formular have to be used for precise computation and the circular constant has to calculate down the 13 places of decimals in order to obtain the precision of 1mm on the ground scale.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.831-841
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• 2017

The irrational number ${\pi}$ is defined as the ratio of circumference of a circle to its radius and always becomes constant. This article does Monte Carlo approximation of its value using the famous Buffon's needle experiment and shows that its convergence is not always proportional to the sample size. We also do Monte Carlo simulations to see the convergence of the computed ${\pi}$ values from the random walk series with independent normal increment. Finally we apply the theoretical derivation to various financial time series data such as KOSPI, stock prices of Korean big firms, global stock indices and major foreign exchange rates. The historical data shows that log transformed data random walk process but most of their first lagged data don't follow a normal distribution. More importantly the computed value from the ratio of the regression coefficient ${\pi}$ tend to converge a constant, unfortunately not ${\pi}$. Using this result we could doubt on the efficient market hypothesis, and relate the degree of the hypothesis with the amount of deviation of the estimated ${\pi}$ values.