• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.86.1-86.1
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• 2015

고대 천문학의 대표적인 관측기기로 혼의가 있다. 중국도 일찍 혼의가 도입되어 천체 관측에 활용된 것으로 보인다. 중국 고대의 선기옥형이라는 기기가 한(漢) 대에 접어 들어 서양에서 도입된 혼천설의 영향을 받아 혼의로 발전하였다. 초창기 혼의에는 주천도수와 24방위의 눈금을 새겼고, 원주율을 3으로 적용하였다. 한말(漢末)에 혼천설에 따라 혼의 안에 지구를 만들고 혼천의 또는 혼천상이라고 불렀다. 혼천설의 구조를 적용하기 위해 비교적 자세한 원주율의 값이 알려지면서 혼의의 정밀한 눈금을 제작하는 계기를 마련하였다. 더불어 수 개의 환을 혼의에 추가하여 2층 구조의 혼의를 개발하였다. 당(唐) 대에 이르러 육합의, 삼신의, 사유의로 구성된 혼의의 3층 구조가 완성되었다. 송(宋) 대에는 혼의와 혼상에 수격식 자동운행장치를 도입하여 혼천의라고 하고, 이전의 관측용 혼의를 동후의(銅候儀)라고 불렀다. 조선 세종 대에 제작한 혼천의는 송(宋) 대의 자동운행이 결합된 혼의였고, 동후의의 관측기능을 대신하여 간의를 사용하였다. 그 재원은 각각 오징의 "서찬언"과 "원사"에서 빌려왔고, 이를 "제가역상집"에 정리하였다. 혼의의 환에는 한 개의 원주에 주천도수, 12시백각, 24방위 중 한 종류의 눈금을 그렸다. 그러나 간의에서는 한 개의 원주에 두 개의 눈금을 그리는 방법이 시작되었다. 이러한 눈금제작 방식은 조선에서 새롭게 개발된 일성정시의에 적용되었다.

• 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.

• 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.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.9-16
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• 2003

This paper aims to investigate how Chinese and Korean evaluate $\pi$ and measure tile area of circle by reviewing the problems in the old mathematical books. The books are Gu-Jang-San-Sul(The nine chapters on tile mathematical art) for China and Gu-Il-Jib for Chosun Dynasty. The result shows that our ancestors used the different values of ${\pi}$ in relation to the accuracy and the various methods for measuring the area of circle.

• Journal for History of Mathematics
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• v.33 no.4
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• pp.223-236
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• 2020

We examine how the formulas of the area and the circumference of a circle related to pi in the ancient Egyptian and the Old Babylonian fields of mathematics have been controversial. In particular, the Great Pyramid of Khufu, Ahmes Papyrus Problem 48 and Moscow Mathematical Papyrus Problem 10 have raised extensive controversy over π. We propose the pi-theory of the Great Pyramid of Khufu as a dynamic symmetry based on Euclid's rectangle. In addition, we argue that the ancient Egyptian or Old Babylonian mathematics influenced Solomon's Molten Sea, Plato and Archimedes' pi.

• 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.

• 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 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 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.6
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• pp.619-624
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• 2012

In this study, we demonstrated the operation of an electroosmotic pump with cylindrical porous glass frits and evaluated its long-term operation. The performance of this electroosmotic pump was characterized in terms of maximum flow rate, current, and pressure using deionized water and 1 mM borate buffer. The maximum flow rate, current, and pressure linearly increase with voltage. The maximum flow rate is normalized by the pumping area and voltage for comparison of the performance between the electroosmotic pumps with cylindrical and planar frits. The normalized maximum flow rate of the cylindrical-type pump is higher than that of the planar-type pump because of their different geometries. The cylindrical-type electroosmotic pump has five times better performance than the planartype electroosmotic pump for a given pump package volume. It can operate stably for over 3 hours.