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

• Communications of Mathematical Education
• /
• v.21 no.3
• /
• pp.451-466
• /
• 2007

Geometry in school mathematics is the field that has the possibility of diverse approach such as Synthetic Geometry and Analytic Geometry. Synthetic Geometry is handled in middle schools and Analytic Geometry in the first year of high schools. Therefore, this research show for the possibility of using Synthetic Geometry in high schools which was learned already in middle schools and the way of integrating both of them concretely. This is expected to help students understand the mathematical meaning of figures a lot.

• Journal of Aerospace System Engineering
• /
• v.16 no.6
• /
• pp.1-7
• /
• 2022

A simulated radar terrain scan data generation method is employed for terrain following. This method scans the discrete terrain by sequentially radiating beams from the radar to the desired scan area with the same azimuth but varying elevation angles. The terrain data collected from the beam is integrated to generate the simulated radar terrain scan data, which comprises radar-detected points. However, these points can be located far from the beam centerline when the radar is far from them due to beam divergence. This paper proposes a geometry-based terrain scan data generation method for analysing simulated radar terrain scan data. The method involves detecting geometric points along the beam centerline, which forms the geometry-based terrain scan data. The analysis of the simulated radar terrain scan data utilising this method confirms that the beam width effects are accounted for in the results.

• Journal for History of Mathematics
• /
• v.18 no.4
• /
• pp.29-38
• /
• 2005

This Paper discusses the history of the conflicts between synthesis and analysis, from those in heuristic and logic development style in ancient Greek to those in projective geometric methods. The two methods, which originally displayed difference in heuristic, offer the base for the two fields of geometry, the analytic geometry and the synthetic geometry in the 18th century as they originated from the field of geometry. As to the 19th century, they even display antagonistic aspects derived by having other perspectives about the true nature of mathematic but finally lose the reason of conflict as the ancient times when the dialectical sublation of both had been proposed.

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

• The Mathematical Education
• /
• v.15 no.1
• /
• pp.5-7
• /
• 1976

Euclid 기하학이 성립하는 공간은 우리들과 가장 밀접한 공간이다. Descartes의 해석기하학은 Euclid의 3차원공간에서 성립한다. 이 경우 점이라 해도 그것은 3개의 실수의 순서쌍(x, y, z)에 의해 표현되는 것으로 생각해도 좋다. 일반의 n차원 Euclid 공간 R$^n$에 대해서도 같은 생각으로 정의할 수 있다. 이 경우 n=1은 수치선, n=2는 평면, n=3은 소위 3차원의 공간으로서 직관적으로 상상할 수 있으나 n(equation omitted)4인 경우는 상상하기 어렵다. 여기서는 거리의 성질과 추상공간을 논하고 Euclid 공간의 거리에서 출발하여 그 성질중 삼각부등식을 계산을 통하여 증명하므로서 공간의 확장화가 이루워짐을 보였다.

• School Mathematics
• /
• v.8 no.2
• /
• pp.215-237
• /
• 2006

In this study, we research distinctive features of geometry problem solving of middle school students whose mathematical achievement levels are distinguished by National Assessment of Educational Achievement. We classified 9 students into 3 groups according to their level : advanced level, proficient level, basic level. They solved an atypical geometry problem while all their problem solving stages were observed and then analyzed in aspect of development of geometrical concepts and access to the route of problem solving. As those analyses, we gave some suggestions of teaching on mathematics as students' achievement level.

• Korean Architects
• /
• no.11 s.439
• /
• pp.82-89
• /
• 2005

• Proceedings of the Korean Society for History of Mathematics Conference
• /
• 2003.11a
• /
• pp.1.2-1.2
• /
• 2003

• Journal for History of Mathematics
• /
• v.3 no.1
• /
• pp.47-70
• /
• 1986