• East Asian mathematical journal
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• v.34 no.2
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• pp.219-238
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• 2018

The purpose of this paper is to reinterpret and visualize Pappus' methods for trisecting the angle by utilizing the Nicomedes' conchoid and Apollonius' symptom of a hyperbola. In particular, we reinterpret the Pappus' three results which are the methods of hyperbola and circle, the trisection of the arc and focus and directrix of the hyperbola by 3 steps(analysis, construction, and proof) in the current middle school curriculum of Mathematics. Moreover, we visualize the construction of an hyperbola which is represented by means of an eccentricity.

• The Mathematical Education
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• v.53 no.3
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• pp.313-327
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• 2014

'Tangent' is one of the most important concepts in the middle and high school mathematics, especially in dealing with calculus. The concept of tangent in the current textbook consists of the ways which make use of discriminant or differentiation. These ways, however, do not present dynamic view points, that is, the concept of variation. In this paper, after applying 'Roberval's way of finding tangent using vectors in terms of kinematics to parabola, ellipse, circle, hyperbola, cycloid, hypocycloid and epicycloid, we will identify that this is the tangent of those curves. This trial is the educational link of mathematics and physics, and it will also suggest the appropriate example of applying vector. We will also help students to understand the tangent by connecting this method to the existing ones.

• The Journal of the Acoustical Society of Korea
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• v.26 no.8
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• pp.415-425
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• 2007

This paper proposes a method of underwater source localization using the wideband interference patterns matching. By matching two interference patterns in the spectrogram, it is estimated a ratio of the range from source to sensor5, and then this ratio is applied to the Apollonius circle. The Apollonius circle is defined as the locus of all points whose distances from two fixed points are in a constant value so that it is possible to represent the locus of potential source location. The Apollonius circle alone, however still keeps the ambiguity against the correct source location. Therefore another equation is necessary to estimate the unique locus of the source location. By estimating time differences of signal arrivals between source and sensors, the hyperbola equation is used to get the cross point of the two equations, where the point being assumed to be the source position. Simulations are performed to get performances of the proposed algorithm. Also, comparisons with real sea experiment data are made to prove applicability of the algorithm in real environment. The results show that the proposed algorithm successfully estimates the source position within an error bound of 10%.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.315-325
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• 2012

Let A and B denote a point, a line or a circle, respectively. For a positive constant $a$, we examine the locus $C_{AB}$($a$) of points P whose distances from A and B are, respectively, in a constant ratio $a$. As a result, we establish some equivalent conditions for conic sections. As a byproduct, we give an easy way to plot points of conic sections exactly by a compass and a straightedge.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.731-744
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• 2010

Nowadays in school mathematics, the skill and method for solving problems are often emphasized in preference to the theoretical principles of mathematics. Students pay attention to how to make an equation mechanically before even understanding the meaning of the given problem. Furthermore they do not get to really know about the principle or theorem that were used to solve the problem, or the meaning of the answer that they have obtained. In contemporary textbooks the conic section such as circle, ellipse, parabola and hyperbola are introduced as the cross section of a cone. But they do not mention how conic section are connected with the quadratic equation or how these curves are related mutually. Students learn the quadratic equations of the conic sections introduced geometrically and are used to manipulating it algebraically through finding a focal point, vertex, and directrix of the cross section of a cone. But they are not familiar with relating these equations with the cross section of a cone. In this paper, we try to understand the quadratic curves better through the analysis of the discussion made in the process of the discovery and eventual development of the conic section and then seek for way to improve the teaching and learning methods of quadratic curves.

• Journal of the Korean Institute of Telematics and Electronics
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• v.8 no.3
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• pp.15-26
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• 1971

The paper presents a new method for analyzing oscillation regions of transistor oscillators. In transistor feedback oscillators oscillation region appears as a circle in feedback impedance complex plane. When the resistive component of feedback impedance is fixed and the reactive component of feedback impedance is varied or vice versa, the locus of maximum negative output conductance becomes hyperbola. In transistor crystal oscillators oscillation region is determined by two circles which make real part and imaginary part of input impedance zero in load impedance complex plane. When the resistive compoment of load impedance is fixed and the reactive colnponent of load impedance is varied or vice versa, the loci of maximum or minimum resistive component of input impedance become straight lines.

• The Journal of the Acoustical Society of Korea
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• v.26 no.8
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• pp.375-380
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• 2007

A reverberation chamber should be designed and constructed so as to satisfy its purposes and available space. However, it is somewhat difficult to meet the intended design requirements due to various errors from construction process. So, the post-construction measurement of its volume and surface areas is very essential to check the actual volume and volume uncertainty of a reverberation chamber These values should be carefully calculated and accurately estimated since they are used not only to evaluate the acoustic characteristics of building materials but also to calculate uncertainties for other acoustic characteristics. In this work, the method for the calculation and uncertainty estimation of the volume of a reverberation chamber is presented. To this end, the coordinates of all corners was measured with Total Station after construction. The results showed that the calculated volume of the measured reverberation chamber differs by 5 % from the design specification. The expanded volume uncertainty was also estimated to be about 2 % of the total calculated volume.