• 한국수학사학회지
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• 제2권1호
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• pp.9-27
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• 1985

Islam toot a great interest in the utility sciences such as mathematics and astronomy as it needed them for the religious reasons. It needeed geometry to determine the direction toward Mecca, its holiest place: arithmetic and algebra to settle the dates of the festivals and to calculate the accounts lot the inheritance; astronomy to settle the dates of Ramadan and other festivals. Islam expanded and developed mathematics and sciences which it needed at first for the religious reasons to the benefit of all mankind. This thesis focuses upon the golden age of Islamic culture between 7th to 13th century, the age in which Islam came to possess the spirit of discovery and learning that opened the Islamic Renaissance and provided, in turn, Europeans with the setting for the Renaissance in 14th century. While Europe was still in the midst of the dark age of the feudal society based upon the agricultural economy and its mathematics was barey alive with the efforts of a few scholars in churches, the. Arabs played the important role of bridge between civilizations of the ancient and modern times. In the history of mathematics, the Arabian mathematics formed the orthodox, not collateral, school uniting into one the Indo-Arab and the Greco-Arab mathematics. The Islam scholars made a great contribution toward the development of civilization with their advanced the development of civilization with their advanced knowledge of algebra, arithmetic and trigonometry. the Islam mathematicians demonstrated the value of numerals by using arithmetic in the every day life. They replaced the cumbersome Roman numerals with the convenient Arabic numerals. They used Algebraic methods to solve the geometric problems and vice versa. They proved the correlation between these two branches of mathematics and established the foundation of analytic geometry. This thesis examines the historical background against which Islam united and developed the Indian and Greek mathematics; the reason why the Arabic numerals replaced the Roman numerals in the whole world: and the influence of the Arabic mathematics upon the development of the modern mathematics.

• 대한수학교육학회지:학교수학
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• 제9권4호
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• pp.523-533
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• 2007

이 논문에서는 피타고라스 정리에 대한 피타고라스와 유클리드의 증명의 의미를 역사적, 수학적 관점에서 고찰하였다. 피타고라스의 닮음비에 의한 증명 방법은 통약성이라는 수에 대한 가정에 근거한 것이라고 볼 수 있다. 반면 유클리드는 통약성이 필요 없는 분해 합동이라는 순수한 기하학적 방법으로 다시 증명하였다. 피타고라스 정리의 증명에서 엿볼 수 있는 피타고라스와 유클리드의 기하에 대한 다른 접근 방식을 현 학교 기하의 바탕이 되는 Birkhoff와 Hither 공리계와 연관하여 논의하였다. Birkhoff는 엄밀하게 정의된 실수 개념을 상식으로 수용하여 현대수학적인 평면 기하 공리계를 제안하였으며, Hilbert는 실수 개념에 의존하지 않는 순수한 기하학을 추구했던 유클리드적 정신을 계승하였다. 따라서 피타고라스 정리에 대한 닮음비와 분해합동을 이용한 증명, 또 넓이에 의한 증명과 넓이가 같음에 의한 증명의 차이는 전통적인 유클리드의 종합기하적 전개와 현대수학적 전개사이의 갈등이라는 기하 교육에서 아직도 완전히 해결되지 않은 논점과 관련이 있다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.1617-1622
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• 1991

Plane sweep is a general method in computational geometry. There are many efficient theoretical algorithms designed using plane sweep technique. However, their practical implementations are still suffering from the topological inconsistencies resulting from the numerical errors in geometric computations with finite-precision arithmetic. In this paper, we suggest new implementation techniques for the plane sweep algorithms to resolve the topological inconsistencies and construct the planar object boundaries from given input curve segments.

• 한국CDE학회논문집
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• 제6권4호
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• 대한수학교육학회지:학교수학
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• 제10권1호
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• pp.123-138
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• 2008

이 연구의 목적은 새수학의 전형이라 할 수 있는 SMSG의 넓이 교수-학습 방식에 대한 비판적 고찰을 통해 새수학 실패의 원인을 교수학적 측면에서 밝히는 것이다. SMSG의 계량도식에 따른 넓이 도입 방식의 독특성에 대해 파악하기 위해 Euclid의 $\ll$원론$\gg$, De Morgan의 $\ll$Elements of arithmetic$\gg$, 그리고 Legendre의 (Elements of geometry and trigonometry) 를 살펴보았다. 또, SMSG의 넓이 교수-학습 방식에 대한 Wittenberg(1963)과 Moise(1963)의 논쟁에 대해 고찰함으로써 초등성과 넓이개념에 대한 심상 형성이 SMSG의 넓이 교수-학습 방식의 성패의 중요한 관건이었다는 점을 확인하였다. 더 나아가 SMSG 넓이 교수-학습 방식이 닮음, 같은 넓이, 통약불가능성등과 같은 수학 내용과의 단절을 초래한다는 점에서 초등성과 기하적 심상의 부재를 낳을 수밖에 없었고, 그것이 SMSG 교수-학습 실패의 원인이라는 것을 보였다.

• 한국분무공학회지
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• 제13권3호
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• pp.134-142
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• 2008

In the case of heavy duty diesel engines, the Urea-SCR system is currently considered to reduce the NOx emission as a proved technology, and it is widely studied to get the high performance and durability. However, the nozzles to inject the urea-water solution into the exhaust pipe occur some problems, including the nozzle clogging, deposition of urea-water solution on the inner wall of the exhaust pipe, resulting in the production of urea salt. In this study, a swirl-type twin-fluid nozzle to produce more fine droplets was used as a method to solve the problems. The effect of the nozzle cap geometry, including the length to diameter ratio ($l_o/d_o$) and chamfer, on the spray characteristics were investigated experimentally. The length to diameter ratio of nozzle cap were varied from 0.25 to 1.125. The chamfer angle of the nozzle cap was constant at 90o. The mean velocity and droplet size distributions of the spray were measured using a 2-D PDA (phase Doppler analyzer) system, and the spray half-width, AMD (arithmetic mean diameter) and SMD (Sauter mean diameter) were analyzed. At result, The larger length to diameter ratio of nozzle cap were more small SMD and AMD. The effect of the chamfer did increase the radial velocity, while it did not affect the atomization effect.

• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.137-144
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• 1998

A common geoboard puzzel serves as the point of departure for an investigation that lends itself to whole-group discussion with a class of prospective secondary school teachers. Students are provided with opportunities to devise and carry out problem-solving strategies (called 'heuristics' by Polya); exploit inerrelationships among geometry, arithmetic and algebra; formulate generalizations and conjectures; plan and execute an computational project; construct mathematical arguments to establish theorems; and find counter-examples to dispose of a false conjecture. In recent tears, Eugene F. Krause wrote two papers having the same title except for the numeral In that papers he arrives at an theorem about the sizes of squares with lattice point vertices in the coordinate plane, In this paper we follow a different path genearlization to coordinate 3-space

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.17-26
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• 2014

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of genus 3 hyperelliptic curves of type $y^2=x^7+ax$ over finite prime fields. The problem of determining the group order of the Jacobian varieties of algebraic curves defined over finite fields is important not only arithmetic geometry but also curve-based cryptosystems in order to find a secure curve. Based on this, we provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety of hyperelliptic curve $y^2=x^7+ax$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ modulo 12. Moreover, we also introduce some implementation results by using our algorithm.

• 한국멀티미디어학회논문지
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• 제20권6호
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• pp.935-949
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• 2017

The purpose of this study was to analyze the characteristics of virtual manipulatives apps that can be used to teach students struggling to learn mathematics. To achieve this goal, ten general characteristics of 23 virtual manipulatives apps were evaluated. The instructional, interface, and interactive design features of apps were also evaluated on five-point scale ratings of 18 items. In addition, SPSS frequency analysis and the correlation between each feature was analyzed. Frequently presented instructional contents among 23 virtual manipulatives apps were geometry, arithmetic operation, number concept and measurement. The frequently presented level of instructional contents was lower grade elementary school and kindergarten age. The frequently presented instructional type was the simulation. Regarding the design features, instructional design was rated as the highest (mean = 3.7); interactive design (mean = 3.6) and interface design (mean = 3.3) were also rated higher than neural. In addition, as the learning strategy was appropriately presented, it was evaluated that there was less screen linkage and content error.

• 한국디지털건축인테리어학회논문집
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• 제7권2호
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• pp.33-41
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• 2007

This thesis aims at understanding Le Corbusier's architecture through study of proportion. Based on the analysis of these texts, four elements - geometry in the outline, diagonal regulation lines in the facade, arithmetic rhythm in the structure, composition in the inner space - were listed. Through these four proportional systems. ten houses of 1920's, designed by Le Corbusier were analysed. The Le Corbusier's proportional system can be classified by two different purposes ; aesthetics and utility standardization for the mass production was reflected. In the later period, the proportion system of 1920's has changed through the process of self-contradiction. But the concept of the golden section and the human scale was reflected on Modulor, which Le Corbusier created in 1940's. Therefore, Le Corbuiser's notion of proportion for harmony of architecture has consistent meaning throughout all of his works from the 1920's.