• 한국수학사학회지
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• 제32권4호
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• East Asian mathematical journal
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• 제37권4호
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• pp.499-521
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• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

• 대한방사성의약품학회지
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• 제2권2호
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• pp.137-142
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• 2016

We have successfully synthesized of 4-cyano-1-(2,4-dichlorophenyl)-5-(4-[$^{11}C$]methoxyphenyl)-N-(piperidin-1-yl)-1H-pyrazole-3-carboxzmide ([$^{11}C$]OMAR), which has been shown a progressing candidate to human brain PET study, from fully automated loop method using ethanol as the only solvent for the entire manufacturing process. The radiochemical yield of [$^{11}C$]OMAR was observed in $4.1{\pm}0.2%$ with $4990{\pm}384Ci/mmol$ of the specific activity and total synthesis time was about 45 minutes after HPLC purification (n = 3, decay corrected) from ethanolic loop system, which was exhibited to better results compared with conventional methods. Ethanolic loop chemistry is favorable and efficient method by simplifies manufacturing procedures as well as satisfied suitable for human administration.

• 원자력산업
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• 제38권5호
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• pp.69-72
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• 2018

• The Korean Journal of Pain
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• 제32권3호
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• pp.231-232
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• 2019

• Bulletin of the Korean Chemical Society
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• 제23권6호
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• pp.896-899
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• 2002

• 대한가정학회:학술대회논문집
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• 대한가정학회 1997년도 Program & Abstracts * The 7th Korea-Japan Home Economics Joint Syposium
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• pp.54-54
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• 1997

• Korean Journal of Radiology
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• 제25권3호
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• pp.314-318
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• 2024

• 대한수학교육학회지:학교수학
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• 제18권3호
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• pp.589-609
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• 2016

본 논문에서는 중세 시대 아랍의 수학자 오마르 카얌(Omar Khayyam)이 제시한 삼차방정식의 기하학적 해법을 현대적으로 재해석하고 두 개의 원뿔곡선을 활용한 삼차방정식의 기하학적 해법이 갖는 교수학적 의미를 고찰하였다. 이를 바탕으로 삼차방정식 $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$, $x^3=ax+b$의 기하학적 해법을 '대수와 기하의 연결', '귀납 및 일반화', '유추를 통한 유사한 해법의 연결' 관점에서 교육적으로 활용할 수 있는 방법과 적용 가능한 교수학적 시사점을 제시하고자 하였다. 삼차방정식을 기하학적으로 해결하면서 '대수와 기하의 연결'의 관점에서 삼차방정식의 대수적 표상과 원뿔곡선이라는 기하학적 표상의 상호 전환을 다룰 수 있다. 또한 '귀납 및 일반화'의 관점에서는 계수 및 상수항이 구체적인 수로 제시된 방정식의 기하학적 해법을 변수가 포함된 삼차방정식의 해법으로 일반화하는 과정을 다룰 수 있으며, '유추를 통한 유사한 해법의 연결'의 관점에서 문제의 해법과 관련된 유사한 절차와 방법을 새로운 문제의 해결에 적용할 수 있는 기회를 제공할 수 있을 것이다.

• 천문학회지
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• 제29권spc1호
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• pp.61-62
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• 1996

The photometry is reported for galaxies in two clusters A1983, 2065 with redshifts 0.046, 0.072 respectively. The luminosity segregation is observed only within a magnitude from the brightest galaxy. The alignment of the galaxy major axis is observed in the Corona Borealis cluster. The intermediate distance clusters (0.05 < z < 0.15) will be studied by CCD mounted on 125cm RCh and 70cm meniscus type telescopes.