삼차방정식에 관한 Omar Khayyām의 기하학적 해법의 재해석과 시각화 - 항이 4개인 삼차방정식의 6가지 -

김향숙,김미연,심효정,박명은,Kim, Hyang Sook,Kim, Mi Yeoun,Sim, Hyo Jung,Park, Myeong Eun 영남수학회 2021 East Asian mathematical journal Vol.37 No.4

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.

Trimethylaluminum (TMA), $NH_3$ 및 TMA :$NH_3$Adduct의 열분해 반응에 대한 in-situ FTIR 분광학적 연구

김향숙,김성한,황진수,최중길,정필조,Hyang Sook Kim,Seong Han Kim,Jin Soo Hwang,Joong Gill Choi,Paul Joe Chong 대한화학회 1993 대한화학회지 Vol.37 No.12

The thermal decomposition of trimethylaluminum (TMA) with ammonia has been investigated by in-situ Fourier transform infrared spectroscopy. The spectroscopic reaction cell, which permits heating interna lly up to 1100$^{\circ}C$, consists of stainless-steel hexagonal-port chamber containing two NaCl windows installed in parallel. In this work, the stoichiometric reaction between TMA and $NH_3$ is found to be completed immediately after mixing. FTIR spectra observed in the range of temperature 25∼1100$^{\circ}C$ show that TMA and TMA : $NH_3$ adduct decompose into methane as a predominant product around 500$^{\circ}C$. The assignments of the IR bands due to the gaseous TMA, $NH_3$ and TMA : $NH_3$ adduct are attempted on the basis of the published data. Furthermore, the decomposition of TMA can be described as a first-order reaction. Kinetic data about the decompositon of TMA and TMA : $NH_3$adduct will also be discussed.

Hetero-Epi막 성장용 사파이어 기판의 산에칭

김향숙,황진수,정필조,Kim, Hyang Sook,Hwang, Jin Soo,Chong, Paul Joe 대한화학회 1995 대한화학회지 Vol.39 No.1

단결정 적층막을 제조하기 위해 사용되는 사파이어 기판에 대하여 황산과 인산의 혼합용액 화학적 에칭을 조사하였다. 여러가지 배향면의 사파이어에 대한 에칭정도는 황산과 인산의 3:1 조성과 $315{\pm}2^{\circ}C$에서 에칭시간에 의존하였다. 280~320$^{\circ}C$ 범위에서 30분간씩 산에칭시킨 후에 에칭속도(R)를 구하였고, log R에 대한 $1/T$ semilog plot로부터 활성화에너지$(E_a)$를 구하였으며, 그것은 $({\bar1}012) > (10{\bar1}0) > (11{\bar2}0) > (0001)$면 순서로 감소하였다. 한편 (0001), $({\bar1}012),\;(10{\bar1}0)$과 $(11{\bar2}0)$면의 표층 두께를 각각 64.6, 46.5, 16.2와 5.1 ${\mu}m$ 에칭시킨 후의 기판 표면을 SEM으로 관찰하였다.

삼차방정식의 기하적 해법에 대한 재조명과 시각화

김향숙,김양,박시은,Kim, Hyang Sook,Kim, Yang,Park, See Eun 영남수학회 2018 East Asian mathematical journal Vol.34 No.4

The purpose of this paper is to reinterpret and visualize the medieval Arab's studies on the geometric methods of solving the cubic equation by utilizing Apollonius' symptom of the parabola. In particular, we investigate the results of $Kam{\bar{a}}l$ $al-D{\bar{i}}n$ ibn $Y{\bar{u}}nus$, Alhazen, Umar al-$Khayy{\bar{a}}m$ and $Al-T{\bar{u}}s{\bar{i}}$ by 4 steps(analysis, construction, proof and examination) which are called the complete solution in the constructions. This paper is available in the current middle school curriculum through dynamic geometry program(Geogebra).

HVPE법에 의한 Zn-Doped GaN 박막 제조

김향숙,황진수,정필조,Kim, Hyang Sook,Hwang, Jin Soo,Chong, Paul Joe 대한화학회 1996 대한화학회지 Vol.40 No.3

For the preparation of single-crystalline GaN film, heteroepitaxial growth on a sapphire substrate was carried out by halide vapor phase epitaxy(HVPE) method. The resulting GaN films showed n-type conductivity. The insulator type GaN film was made by doping with Zn(acceptor dopant), which showed emission peaks around 2.64 and 2.43 eV. The result of this study indicates that GaN can be obtained in an epitaxial structure of MIS(metal-insulator-semiconductor) junction. The observed data are regarded as fundamental in developing GaN epitaxial films for light emitting devices of hetero-structure type.

중세 이슬람이 보인 입방배적문제 해결방법들의 재조명과 시각화

김향숙,박진석,이은경,이재돈,하형수,Kim, Hyang Sook,Pak, Jin Suk,Lee, Eun Kyoung,Lee, Jae Don,Ha, Hyoung Soo 영남수학회 2014 East Asian mathematical journal Vol.30 No.2

This study, utilizing several features about plane figures covered in the current secondary curriculum of mathematics and reviewing two solutions to cube duplication problem presented by Menaechmus, proving the solution by Nicomedes and visualizing solutions based on Apollonius' 'Conics' by medieval Islam geometricians such as Ab$\bar{u}$ Bakr al-Haraw$\bar{i}$, AbAb$\bar{u}$ J$\acute{a}$far al-Kh$\bar{a}$zin, Nas$\bar{i}$r al-D$\bar{i}$n al-T$\bar{u}s\bar{i}$, Y$\bar{u}$suf al-Mu'taman ibn H$\bar{u}$d, introduce to teachers and students in the field where the question of cube duplication problem comes from and which solving method has developed it and suggests new methods for visualization using dynamic geometry program as well so that the contents reviewed can be used in the filed. The solving methods to cube duplication problem in this paper are very creative and increase the practicality, efficiency and value of Mathematics, and provide students and teachers with the opportunities to reconfirm the importance and beauty of basic knowledge in the secondary geometry in the process of visualization of drawing figures using dynamic geometry program.

Pappus 가 보인 일반각의 3등분문제 해결의 재조명과 시각화

김향숙,김양,박진석,Kim, Hyang Sook,Kim, Yang,Pak, Jin Suk 영남수학회 2018 East Asian mathematical journal Vol.34 No.2

The purpose of this paper is to reinterpret and visualize Pappus' methods for trisecting the angle by utilizing the Nicomedes' conchoid and Apollonius' symptom of a hyperbola. In particular, we reinterpret the Pappus' three results which are the methods of hyperbola and circle, the trisection of the arc and focus and directrix of the hyperbola by 3 steps(analysis, construction, and proof) in the current middle school curriculum of Mathematics. Moreover, we visualize the construction of an hyperbola which is represented by means of an eccentricity.

두류 , 곡류 및 감자전분의 호화 특성

김향숙,안승요 ( Hyang Sook Kim,Seung Yo Ahn ) 한국식품조리과학회 1994 한국식품조리과학회지 Vol.10 No.1

Studies were carried out to investigate physicochemical and gelatinization properties of legume, cereal and potato starches. Cowpea, mung bean, acorn, and buckwheat starches showed similar moisture content and amylose content, however, there is neither similarity nor certaion trend in WBC, swilling power, and solubility among them. DSC thermograms of cowpea, mung bean, acorn, and buckwheat starches showed similar patterns with two endothermic peaks and relatively broad gelatinization ranges. SEM photomicrography of gelatinized cowpea, mung bean, acorn and buckwheat starches showed highly swollen and extremely disintegrated, folded structure.

격자다면체 부피에 대한 역사적 고찰 및 그 응용 - 수열 단원에의 응용 -

김향숙,하형수,Kim, Hyang-Sook,Ha, Hyoung-Soo 한국수학사학회 2010 Journal for history of mathematics Vol.23 No.2

This article includes an introduction, a history of Pick's theorem on lattice polyhedron and its proof, Reeve's theorem on 3-dimensional lattice polyhedrons extended from the Pick's theorem and Ehrhart polynomial generalized as an n-dimensional lattice polyhedron, and then shows the relationship between the volume of 3-dimensional polyhedron and the number of its lattice points by means of Reeve's theorem. It is aimed to apply the relationship to the visualization of sums in sequences.

대수와 기하의 수학적 연결성 지도를 위한 Khayyam과 Al-Kāshi의 문제 해결 방법 재조명 및 시각화

김향숙,박시은,Kim, Hyang Sook,Park, See Eun 영남수학회 2021 East Asian mathematical journal Vol.37 No.4

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.