• Journal for History of Mathematics
• /
• v.25 no.4
• /
• pp.37-51
• /
• 2012

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

• Communications of Mathematical Education
• /
• v.20 no.4 s.28
• /
• pp.621-634
• /
• 2006

In this study we describe the characteristics of solving geometry problems related with the ratio of segments using the principle of the lever and the center of gravity, compare and analyze this problem solving method with the traditional Euclidean proof method and the analytic method.

• School Mathematics
• /
• v.10 no.4
• /
• pp.573-581
• /
• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Journal for History of Mathematics
• /
• v.15 no.2
• /
• pp.15-32
• /
• 2002

The first part of this thesis gives some brief explanation of the theory and history of imaginary elements in analytic geometry in the 19th century. The second part of this thesis discusses the theory of imaginary elements of synthetic geometry in the first half of the 19th century. Then the next part mentions the theory of imaginary elements of geometry in the second half of that same century. Particularly Christian von Staudt's and Felix Klein's theories are handled in this part. Von Staudt, who has completed the system of the synthetic projective geometry, used ‘involution’ in order to introduce a new concept ‘imaginary elements’- imaginary points, imaginary lines and imaginary plane-in synthetic geometry. Klein applied von Staudt's theory as he convey the result of the research in algebraic geometry in a picture. Von Staudt's and Klein's research may be regarded as the top of the effort to investigate possible relationship between real and imaginary structures.

• Journal of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1103-1137
• /
• 2022

Our motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finiteness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyperharmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1999.05a
• /
• pp.15-15
• /
• 1999

• Proceedings of the Korean Nuclear Society Conference
• /
• 1999.10a
• /
• pp.52-52
• /
• 1999

• Journal of the Korean School Mathematics Society
• /
• v.18 no.4
• /
• pp.411-429
• /
• 2015

In this study we investigated the effects of using GSP in solving geometric problems. Especially we focused the effects of GSP in leveled students' connection of geometry and algebra. High leveled students prefer to use algebraic formula to solve geometric problems. But when they did not know the geometric meaning of their algebraic formula, they could recognize the meaning after using GSP. Middle and low leveled students usually used GSP to obtain hints to solve the problems. For the low leveled students GSP was usually used to understand the meaning of the problem, but it did not make them solve the problem.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2008.03a
• /
• pp.243-246
• /
• 2008

This paper is to consider analytical thermodynamic modeling of bipropellant propulsion system. The objective of thermodynamic modeling is to predict thermodynamic conditions such as pressures, temperatures and densities in the pressurant tank and the propellant tank in which heat and mass transfer occur. In this paper also it shows analytic equations that calculate the evolution of ullage volume and interface areas. Since the ullage interface areas are time-varying,(the liquid propellant volume decreases as the rocket engine is firing; the change of ullage volume correspond to the change of liquid propellant volume) for a numerical convenience non-dimensionalized correlations are commonly used in most literatures with limitations; a few percentages of inherent error. The analytic equations are derived from analytic geometry, subsequently without inherent error. Those equations are important to calculate the heat transfer areas in the heat transfer equations. It presents the comparison result of both analytic equations and correlation method.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.430-430
• /
• 2000

This paper presents a new analytic approach using tetrahedrons to determine the forward kinematics of the 3-6-type Stewart platform. By using of the tetrahedral geometry, this approach has the advantage of greatly reducing the complexity of formulation and the computational burden required by the conventional methods which have been solved the forward kinematics with three unknown angles. As a result, this approach allows a significant abbreviation in the formulations and provides an easier means of obtaining the solutions. The proposed method is well verified through a series of numerical simulation.