• East Asian mathematical journal
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• v.36 no.2
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• pp.131-146
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• 2020

The isoperimetric problem is a well-known optimization problem from ancient Greek. Among plane figures with the same perimeter, which is the largest area surrounded? The answer to the question is circle. Zenodorus and Steiner's pure geometric proofs, which left a lot of achievements in this matter, looked beautiful with ideas at that time. But there was a fatal flaw in the proof. The weakness is related to the existence of the solution. In this paper, from a view of the existence of the solution, we investigate proofs of Zenodorus and Steiner and get educational implications.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.

• Archives of design research
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• v.16 no.2
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• pp.121-130
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• 2003

The diffusion expressive power means the flexibility of which creative power test spheres(fluency, originality) by Torrance is ability making the considerations, thoughts and concepts to the meaningful symbolic change. This study is willing to develop and improve program toward the diffusion expressive power and is to testify training effect of the students are majoring design with the object. The training programs composed of six levels which is based on the theory of Eskild Tjalve. And the parameters of each levels are element, function, number, arrangement, form geometric, size and have to practice 2 weeks at once by 12 weeks. For successful measuring the effective results of this study, 40 undergraduate junior students in the department of design are grouped to excercise with experimental pilot group and regulated group. The standard type of creative paper is used to evaluate the results of student's training. This study give proof that creative power of the experimental pilot and under training group is higher than the regulated and under comparison group at in the conclusion.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.55-70
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• 2008

This study is about the Data which is one of Euclid's writing. It dealt with the organization of contents, formal system and mathematical meaning. First, we investigated the organization of contents of the Data. Second, on the basis of this investigation, we analyzed the formal system of the Data. It contains the analysis of described method of definition, proposition, proof and the meaning of 'given'. Third, we explored the mathematical meaning of the Data which can be classified as algebraic point of view, geometric point of view and the opposite point of view to 'The Elements'.

• East Asian mathematical journal
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• v.32 no.4
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• pp.483-500
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• 2016

Ancient Greek mathematician Euclid left three books about mathematics. It's 'The elements', 'The data', 'On divisions of figure'. This study is based on the analysis of Euclid's 'On divisions of figure'. 'On divisions of figure' is a book about the construction of the shape. Because, there are thirty six proposition in 'On divisions of figure', among them 30 proposition are for the construction. In this study, based on the 'On divisions of figure' we explore the direction for construction education. The results were as follows. First, the proposition of 'On divisions of figure' shall include the following information. It is a 'proposition presented', 'heuristic approach to the construction process', 'specifically drawn presenting', 'proof process'. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of 'On divisions of figure' is 'The elements'. 'The elements' includes the construction propositions 25%. However, the geometric constructions contents in middle school area is only 3%. Therefore, it is necessary to expand the learning of construction in the our country mathematics curriculum.

• The Mathematical Education
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• v.37 no.1
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• pp.35-54
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• 1998

Half century has passed since Korean peninsula was divided into South and North Korea. Now a days, there are many differences of politics, economy, culture and education between South and North Korea. Especially mathematics education in which I am interested has a lot of changes and differences. This is proved true by defects' proof. For those reasons, I compared South Korea's education ideology, goal and system, and goals of mathematics education with North Korea's. I compared geometric(1-4 years, published by Pyong-yang Educational Book Publication Co. 1991) of mathematics texts(1-6 years) which are used in the secondary school with mathematics text of South Korea in contents and organization of them. As a result of this comparison, education ideology and goal are distinctly different from those of South Korea because of the difference of pursuing humanity. In North Korea, the curriculum is very strict without autonomy. There are 1283 mathematics classes which are occupied 19% for six years during the secondary school. The contents are very similar, but there is a little difference in the definition of a term. The problems which praise Kim Il-sung and his son and reveal loyalty to them were found, and there were a lot of problems in order to promote hostile feeling against U.S.A and South Korea, too. In conclusion, mathematics education of Korean peninsula should be reunified in the fields of the terms and contents at first.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.57-73
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• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.175-184
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• 1998

The purpose of this study is that the Van Hiele theory can be applied to even vocational high school students. Through the comparison of Van Hiele level distribution of middle school students and high school students, it is that the aims of this study is to study the geomatric level of vocational high school students and to analize them, even so it can be to find for them the effective method of Geomatric education The subject of study is three kinds of vocational high school - commercial high school, industrial high school, fisheries high school - boys (240), girls (120) in Boryeong city, Chungchong Nam Do. We referred to Kim Mi-cheong′ thesis(1994) and Cheong Yean-sok′s thesis(1992) and compared my result with them. The method and the process of the study were based on the th method of CDASSG project. And we used Van Hiele Level Test as an instrument of measurement. We got the following conclusion as the result of the study 1. The 86％ of the subject of the study was applied to the theory of Van Hiele - "Any students can reach level n just through level n-1." Even so the propriety of the theory proved to be from this study again. 2. The 88% of the subject of the study is applicable to below level 2. So if the proof is introduced to them in the class, it was very difficult for them to understand it. 3. The geometric level of vocational high school students is the same as the second grade of middle school. But we think to be desirable that a basic concept puts first in importance through recomposed teaching materials, because 68% of the students is seldom changed at level 1.

• School Mathematics
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• v.11 no.1
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• pp.55-70
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• 2009

The purpose of this study is to implement Lakatos method in the teaching and learning of geometry for middle school students. In his landmark book , Lakatos suggested the following instructional approach: an initial conjecture was produced, attempts were made to prove the conjecture, the proofs were repeatedly refuted by counterexamples, and finally more improved conjectures and refined proofs were suggested. In the study, students were selected from the high achieving students who participated in the special mathematics and science program offered by the city council of Seoul. The students were given a contradictory geometric proposition, and expected to find the cause of the fallacy. The students successfully identified the fallacy following the Lakatos method. In this process they also set up a primitive conjecture and this conjecture was justified by the proof and refutation method. Some implications were drawn from the result of the study.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.