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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Journal for History of Mathematics
Journal Basic Information
Journal DOI :
The Korean Society for History of Mathematics
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Volume & Issues
Volume 21, Issue 4 - Nov 2008
Volume 21, Issue 3 - Aug 2008
Volume 21, Issue 2 - May 2008
Volume 21, Issue 1 - Feb 2008
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Theory of Capillarity of Laplace and birth of Mathematical physics
Lee, Ho-Joong ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 1~30
The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions
represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.
Bolzano and the Evolution of the Concept of Infinity
Cheong, Kye-Seop ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 31~52
The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.
The historical developments process of the representations and meanings for ratio and proportion
Park, Jung-Sook ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 53~66
The concepts of ratio and proportion are familiar with students but have difficulties in use. The purpose of this paper is to identify the meanings of the concepts of ratio and proportion through investigating the historical development process of the meanings and representations of them. The early meanings of ratio and proportion were arithmetical meanings, however, geometrical meanings had taken the place of them because of the discovery of incommensurability. After the development of algebraic representation, the meanings of ratio and proportion have been growing into algebraic meanings including arithmetical and geometrical meanings. Through the historical development process of ratio and proportion, it is observable that the meanings of mathematical concepts affect development of symbols, and the development of symbols also affect the meanings of mathematical concepts.
Development of the Integral Concept (from Riemann to Lebesgue)
Kim, Kyung-Hwa ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 67~96
In the 19th century Fourier and Dirichlet studied the expansion of "arbitrary" functions into the trigonometric series and this led to the development of the Riemann's definition of the integral. Riemann's integral was considered to be of the highest generality and was discussed intensively. As a result, some weak points were found but, at least at the beginning, these were not considered as the criticism of the Riemann's integral. But after Jordan introduced the theory of content and measure-theoretic approach to the concept of the integral, and after Borel developed the Jordan's theory of content to a theory of measure, Lebesgue joined these two concepts together and obtained a new theory of integral, now known as the "Lebesgue integral".
A math-historical outlook on etymology of korean number words: from hana(one) to yoel(ten)
Park, Kyo-Sik ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 97~112
In this study, the research results up to now on original word form and its meaning of Korean number words hana, dul, ..., yeol are looked out from math-historically. In fact, finding out original word form and its meaning of hana, dul, and set(ses) may not be possible in the respect of history of mathematics. There might have been a gap between set(ses) and net(nes), and between net(nes) and daseot(daseos). Original word form and its meaning of hana, dul, set(ses), and net(nes) must be found out in different aspect from those of daseot(daseos), yeoseot(yeoseos), ..., yeol. There might have been a gap between yeoseot(yeoseos) and ilgop(ilgob). Coining number word mechanism for ilgop(ilgob), yeodeol,(yeodeolb) and ahop(ahob) might have been same each other. There might have been a gap between ahop(ahob) and yeol. The research results up to now have not paid attention to this gaps sufficiently. But according to history of mathematics, there must have existed several gaps.
ABC conjecture and iteration of polynomials
Choi, Eun-Mi ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 113~126
This work is devoted to study about the abc conjecture: how it works in the development of the proof of Fermat's last theorem and more generally in the diophantine equation theory. And it is also studied the application of the abc conjecture to the iteration of polynomials.
Four proofs of the Cayley formula
Seo, Seung-Hyun ; Kwon, Seok-Il ; Hong, Jin-Kon ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 127~142
In this paper, we introduce four different approaches of proving Cayley formula, which counts the number of trees(acyclic connected simple graphs). The first proof was done by Cayley using recursive formulas. On the other hands the core idea of the other three proofs is the bijective method-find an one to one correspondence between the set of trees and a suitable family of combinatorial objects. Each of the three bijection gives its own generalization of Cayley formula. In particular, the last proof, done by Seo and Shin, has an application to computer science(theoretical computation), which is a typical example that pure mathematics supply powerful tools to other research fields.
Student's difficulties in the teaching and learning of proof
Kim, Chang-Il ; Lee, Choon-Boon ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 143~156
In this study, we divided the teaching and learning of proof into three steps in the demonstrative geometry of the middle school mathematics. And then we surveyed the student's difficulties in the teaching and learning of proof by using of questionnaire. Results of this survey suggest that students cannot only understand the meaning of proof in the teaching and learning of proof but also they cannot deduce simple mathematical reasoning as judgement for the truth of propositions. Moreover, they cannot follow the hypothesis to a conclusion of the proposition It results from the fact that students cannot understand clearly the meaning and the role of hypotheses and conclusions of propositions. So we need to focus more on teaching students about the meaning and role of hypotheses and conclusions of propositions.
Analysis for the changes of the mathematics cognitive domain and for the international achievement in TIMSS
Kim, Sun-Hee ;
Journal for History of Mathematics, volume 21, issue 3, 2008, Pages 157~182
TIMSS 2003 is the third and most recently round of IEA's Trends in International Mathematics and Science Study. In this study, I considered the changes of the mathematics cognitive domain in TIMSS and got some facts for developing assessment framework. And I analyzed 7 countries' achievement in the view of our country Korea, i.e. Singapore, Hongkong, Chinese Taipei, Japan, Netherlands, and Unites States. With the reliable and valid achievement scales for cognitive domains given by ISC, students' achievement scales were analyzed according to country, percentile, and sex in each cognitive domain.