• Communications of Mathematical Education
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• v.15
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• pp.17-22
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• 2003

현재 각 대학의 사범대학에서는 저마다의 교과과정에 의하여 기하교육을 하고 있다. 해석학이나 대수학에 비하여 매우 다양하게 운영되고 있는 기하학 강좌 내용에 대하여 우선 몇 군데 대학에서의 기하학개론 및 미분기하학 강좌 내용을 비교하고, 교사 양성기관에서의 기하학 개론과 미분기하학 강좌에서 다루어야 할 필수 요소를 알아보고자 한다.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.221-221
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• 2010

고대의 인도수학은 산스크리트어로 쓰여 있고, 최초의 기하학은 베다문헌으로 경전 속에 포함되어 있으며, 성스런 제단이나 사원을 설계하기위해서 발전하였다. 고대 인도의 많은 수학자들은 힌두교의 성직자들로 일찍이 십진법, 계산법, 방정식, 대수학, 기하학, 삼각법 등의 연구에 공헌하였다. 인도 기하학은 양적이며 계산적이지만 원리를 가지고 문제를 해결하는 특성이 있다. 그러나 고대 그리스 기하학은 공리적이고 연역적으로 전개되는 완전한 학문으로 발전하였다. 고대 인도와 타 문명권의 기하학을 비교하는 것은 오늘날 문제해결을 중시하는 현대과학의 시대에 가치와 의미가 있는 것으로 사료된다.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• Proceedings of the Korean Society for History of Mathematics Conference
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• 1997.11a
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• pp.1-1
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• 1997

• Journal for History of Mathematics
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• v.21 no.1
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• pp.109-120
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• 2008

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. However, a mechanical computation-oriented instruction or a formal concept-oriented instruction is difficult and dull for most students. In this context, how to teach mathematical concepts successfully is a very serious problem. As a solution for this problem, we suggest establishing original concepts in linear algebra from the students' point of view. Any original concept means not only a practical beginning for the historical order and theoretical system but also plays a role of seed which can build most of all the important concepts. Indeed, linear algebra has exactly two original concepts : geometry of planes, spaces and linear equations. The former was investigated in [2], the latter in the present paper.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.715-730
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• 2016

The purpose of this study is to analyze Descartes's point of view on the mathematical connection of algebra and geometry which help comprehend the traditional frame with a new perspective in order to access to unsolved problems and provide useful pedagogical implications in school mathematics. To achieve the goal, researchers have historically reviewed the fundamental principle and development method's feature of analytic geometry, which stands on the basis of mathematical connection between algebra and geometry. In addition we have considered the significance of geometric solving of equations in terms of analytic geometry by analyzing related preceding researches and modern trends of mathematics education curriculum. These efforts could allow us to have discussed on some opportunities to get insight about mathematical connection of algebra and geometry via geometric approaches for solving equations using the intersection of curves represented on coordinates plane. Furthermore, we could finally provide the method and its pedagogical implications for interpreting geometric approaches to cubic equations utilizing intersection of conic sections in the process of inquiring, solving and reflecting stages.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.13-26
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• 2009

Elie Cartan is one of the mathematicians whose works marked the development of geometry and algebra of 20th century. We illuminate his mathematical contributions which is familiar to the experts but is alien to most of the mathematicians in general. Also we elucidate some of his influences.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.15-20
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• 1979

본(本) 논문(論文)에서는 smooth Affine variety가 미분가능(微分可能) 다양체(多樣體)임을 보임으로써 대수기하학(代數幾何學)이 다양체이론(多樣體理論)과 관련(關聯)됨을 논(論)하였다. $\S1$에서는 affine variety의 차원(次元)과 affine variety의 접공간(接空間)에 대(對)한 정의(正義)와 그에 관련(關聯)된 성질(性質)들을 논(論)하였고 $\S2$에서는 simple point와 국소(局所) 매개변수(媒介變數), 그리고 ${\Theta}_x$에서의 유리함수의 급수(級數) 등(等)을 이용(利用)하여 주정리(主定理)(정리(定理)9)를 증명(證明)하였다.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.15-29
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• 2011

This study was carrying out research on the geometry of Sulbas${\={u}}$tras as parts of looking for historical roots of oriental mathematics, The Sulbas${\={u}}$tras(rope's rules), a collection of Hindu religious documents, was written between Vedic period(BC 1500~600). The geometry of Sulbas${\={u}}$tras in ancient India was studied to construct or design for sacrificial rite and fire altars. The Sulbas${\={u}}$tras contains not only geometrical contents such as simple statement of plane figures, geometrical constructions for combination and transformation of areas, but also algebraic contents such as Pythagoras theorem and Pythagorean triples, irrational number, simultaneous indeterminate equation and so on. This paper examined the key features of the geometry of Sulbas${\={u}}$tras and the geometry of Sulbas${\={u}}$tras for the construction of the sacrificial rite and the fire altars. Also, in this study we compared geometry developments in ancient India with one of the other ancient civilizations.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.103-121
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• 2017

Taxicab geometry was a typical non-Euclid geometry for mathematically gifted. Most educational material related quadratic curves on taxicab geometry for mathematically gifted served them to inquire the graph of the curves defined by focis and constant. In this study, we provide a shape of quadratic curves on taxicab geometry by applying three definitions(geometric algebraic definition, eccentricity definition, conic section definition).