• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.9-18
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• 2006

In this paper we study on concept analogy of altitude and escribed circle of triangle. We start from following theorems related with sides of triangle: existence of triangle, Pythagoras theorem, cosine theorem, Heron formula. Using concept analogy of sides-altitudes, altitudes-escribed circle's radii we discover some properties of altitude and escribed circle's radii and prove these properties.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.257-262
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• 2014

In this note we consider "generalized Riesz points" for compact and quasinilpotent perturbations of Toeplitz operators acting on the Hardy space of the unit circle.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.6
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• pp.782-786
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• 2010

Thrust deduction related to the prediction of power performance of a ship is rather resistance increase, and as a preliminary study for it forces upon a circular cylinder in a uniform flow of ideal fluid due to singularities located behind it are investigated. The circle theorem is used to get the complex velocity potential for the flow field under consideration, and the Blasius theorem is applied to obtain forces upon the circular cylinder. As singularities sinks, point vortices and dipoles and their combinations are treated. $\varepsilon$, standing for the strength of a singularity, and $\delta$, representing the distance between the cylinder and the singularity, are important small parameters for the resistance and lateral forces. For sinks or point vortices it is shown that the dimensionless forces upon the cylinder is O($\epsilon$) if $\epsilon$= O($\delta$) is assumed, and the same holds for dipoles if $\epsilon$= O(${\delta}^3$) is supposed. Forces upon the cylinder by a symmetric pair of sinks are greater than a single sink located at the central plane since there is an additional term due to cross effects, and the same is also valid for the case of dipole. Combination of dipole and a point vortex is also considered and a few new aspects are clarified.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.1-16
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• 2002

The area between the arc and chord of a circle is called Hosichun whose figure looks like a bow and an arrow, and had been evaluated by the two formulas $\textit{H}_{n1}$=a(a＋y)/2 and $\textit{H}_{n2}$=3ay/4, where $\alpha$ is the length of the arrow and y the chord of the circle. By the inspection of the area of the Hosichun, some errors of the numeration table in Thurmans S. Peterson's CALCULUS were found easily, that is, the area of the Hosichun is smaller than its subarea in the same Hosichun and perhaps has been to be the worldwide and centurial invalid standard. From now on, the chain proofreadings of the errors will be necessary in our mathematical world. This paper is intended to introduce some such problems related to a circle and another Pythagorean Theorem which is the ratio of the side and diagonal of five and seven In a square.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.253-264
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• 2017

We first extend Yano-Nomizu's theorem, which characterizes extrinsic spheres in a Riemannian manifold, for Riemannian maps. Then we introduce Clairaut Riemannian maps, give an example and obtain necessary and sufficient conditions for a Riemannian map to be Clairaut type.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.95-107
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• 1998

In this paper we prove the Hopf-Rinow theorem for CAT(0) spaces and show that the ideal boundaries of complete CAT(0) manifolds of dimension 2 or 3 with some additional conditions are homeomorphic to the circle or 2-sphere by the characterization of the local shadows around the branch points.

• Journal for History of Mathematics
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• v.1 no.1
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• pp.1-8
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• 1984

본 논문에서는 수학적인 사유형식을 시기적으로 수평과 수직의 축에서 관찰할 목적으로 Descartes의 원정리을 생각한다. 이 정리에 잔해서는 지금까지 접척원의 곡률의 연구가 있으며, 특히 내접원, 외접원의 곡률을 중심적으로 수많은 방법으로 다루어지고 있다. 분 논문에서 이들 방법을 일반화하여 고찰하며 특히 독립적으로 연구되어온 화산의 방법과 비교한다.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.251-274
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• 2020

We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the Farey map on the unit interval which generates an additive continued fraction algorithm. We explore some number theoretical properties of the Romik system. In particular, we prove an analogue of Lagrange's theorem in the case of the Romik system on the unit quarter circle, which states that a point possesses an eventually periodic digit expansion if and only if the point is defined over a real quadratic extension field of rationals.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.943-960
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• 2018

Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.

• The Mathematical Education
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• v.53 no.4
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• pp.509-524
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• 2014

This study was to investigate the types of errors and the frequency of errors to understand students' solving process on the descriptive items with the students of an excellent high school which located in a non-leveling local school district of Gyunggi Province. All 11 items were developed in the equation of a circle and 120 students who attended this high school participated in solving them. The result showed a tendency as follows: Logically invalid inference(Type A, 38.83%) of errors, Omission error of the problem solving process(Type B, 25%), Technical error(Type C, 15.67%), Wrong conclusion(Type D, 11.94%), Use of wrong theorem(Type E, 5.97%), and Use of wrong picture(Type F, 2.61%). The logically invalid inference the students showed with a largest tendency was made because of the lack of reflection. This meant that this error could be corrected in a little treatment of carefulness.