• Journal for History of Mathematics
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• v.19 no.1
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• pp.79-90
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• 2006

The purpose of this paper is to derive the ratios of trigonometric special angles from Euclid's by constructing regular pentagon and decagon. The intention of this paper is started from recognizing that teaching of the special angles in secondary math classroom excessively depends on algebraic approaches rather geometric approaches which are the origin of the trigonometric ratios. In this paper the method of constructing regular pentagon and decagon is reviewed and the geometric relationship between this construction and trigonometric special angles is derived. Through such geometric approach the meaning of trigonometric special angles is analyzed from a geometric perspective and pedagogical ideas of teaching these trigonometric ratios is suggested using history of mathematics.

• Journal for History of Mathematics
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• v.30 no.4
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• pp.221-232
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• 2017

In this paper, we discuss how ancient Egyptians find out the area of the circle based on $\ll$Ahmose Papyrus$\gg$. Vogel and Engels studied the quadrature of the circle, one of the basic concepts of ancient Egyptian mathematics. We look closely at the interpretation based on the approximate right triangle of Robins and Shute. As circumstantial evidence for Robbins and Shute's hypothesis, Egyptians prior to the 12th dynasty considered the perception of a right triangle as examples of 'simultaneous equation', 'unit of length', 'unit of slope', 'Egyptian triple', and 'right triangles transfer to Greece'. Finally, we present a method to utilize the squaring the circle by ancient Egyptians interpreted by Robbins and Shute as the dynamic symmetry of Hambidge.

• East Asian mathematical journal
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• v.34 no.4
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• pp.371-402
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• 2018

The researchers set up a research question to find out how to teach the concept of a right triangle through classification activities after listening to the conversations of fellow teachers about the recently revised textbooks. First, a questionnaire was created to confirm the objectivity of the research problem, data were collected through online and offline, and interviews were conducted with some of the respondents. As a result, it confirmed that there was a considerable difference in the perception of the research study about the direction of revising the curriculum called 'student participation centered' and 'the possibility of achieving the learning objective'. Then, we analyzed the critical interpretations used in the third grade math textbook Lesson 2. 'Plane Figure' part 4 and 5. Finally, by analyzing the results of the recognition analysis and textbook analysis, we proposed two learning methods which can link the triangle classification activity and the right triangle concept. Based on the results of the research, we obtained suggestions that a teaching should be made regarding that the classification process may be changed according to the student's prior knowledge and the process of classification activities may be different according to the viewpoint and classification criteria.

• Journal of the Korea Society of Computer and Information
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• v.16 no.6
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• pp.179-186
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• 2011

This paper suggests the minimum number of vertex guards algorithm. Given n rooms, the exact number of minimum vertex guards is proposed. However, only approximation algorithms are presented about the maximum number of vertex guards for polygon and orthogonal polygon without or with holes. Fisk suggests the maximum number of vertex guards for polygon with n vertices as follows. Firstly, you can triangulate with n-2 triangles. Secondly, 3-chromatic vertex coloring of every triangulation of a polygon. Thirdly, place guards at the vertices which have the minority color. This paper presents the minimum number of vertex guards using dominating set. Firstly, you can obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, you can obtain dominating set from visibility graph or visibility matrix. This algorithm applies various art galley problems. As a results, the proposed algorithm is simple and can be obtain the minimum number of vertex guards.

• Journal of the Korea Society of Computer and Information
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• v.11 no.4 s.42
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• pp.189-196
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• 2006

The ABS method which is modeling the shape-design helps designers concentrate upon the design intuitively, using the modeling method based on the geometrical characteristics, the property information (a point. a curve. slopes. etc.). For the multi-sided patches, the ABS Modeling attempts the modeling with the uniform domain like a right triangle and a regular square. The mentioned method can reduce the speed of modeling but it can cause the difference from a designer's intention in the process of interpolation between the attributes for object modeling. Therefore, in this paper. we propose ABS modeling based on the Chordlength domain method to minimize such differences. The Chordlength, one of the methods generating irregular domain. is the technique transforming the domain in accordance with the length and form of attributes which a shape consists of. The Chordlength domain method is performed using MEL.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.5
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• pp.431-436
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• 2003

In this paper, simulation results of an electromagnetic field and mode distributions in a cylindrical reverberation chamber were presented. Reverberation chamber is an alternative test facility for a semi anechoic chamber, which is widely used for the analysis and measurement of electromagnetic interference and immunity tests. The method of computing the number of modes in a cylindrical reverberation chamber was presented and the number of modes in a cylindrical reverberation chamber with the same volume was compared with the different ratio of radius to height. The FDTD method was used to produce field characteristics inside of rectangular, right-angled isosceles triangular, and cylinder type reverberation chambers with the same test volume.

• Korean Journal of Remote Sensing
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• v.16 no.1
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• pp.99-108
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• 2000

The purpose of this paper is to combine digital elevation models (DEM) using SPOT satellite stereo images. After DEM extraction, a grid of longitude and latitude is generated using the results of DEM extraction. Heights at each grid location are determined from the obtained DEMs by using triangular image warping interpolation that uses the heights of the three nearest neighbors. The final heights at each grid location can then be determined by using the maximum likelihood as a fusion strategy. The input images used in this paper are two pairs of SPOT stereo images and experiments show that heights of DEM are successfully fused

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.28 no.3
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• pp.72-84
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• 2010

This study was attempted in order to offer basic data for implementing and applying Samjonseokjo(三尊石造), which is one of traditional stone construction method, by confirming how the constructive principle is expressed such as proportional beauty, which is contained in the modeling of Triad of Buddha Carved on Rock that was formed in the period of the Three States, centering on Triad of Buddha Carved on Rock in Susan. The summarized findings are as follows. 1. As a result of analyzing size and proportion of totally 17 of Triad of Buddha Carved on Rock, the average total height in Bonjonbul(本尊佛) was 2.96m. Right Hyeopsi(右挾侍) was 2.19m. Left Hyeopsi(左挾侍) was 2.16m. The height ratio according to this was 100:75:75, thereby having shown the relationship of left-right symmetrical balance. The area ratio in left-right Hyeopsi was 13.4:13.7, thereby the two area having been evenly matched. 2. The Triad of Buddha Carved on Rock in Seosan is carved on Inam(印岩) rock after crossing over Sambulgyo bridge of the Yonghyeon valley. Left direction was measured with $S47^{\circ}E$ in an angle of direction. This is judged to target an image change and an aesthetic sense in a Buddhist statue according to direction of sunlight while blocking worshipers' dazzling. 3. As for iconic characteristics of Buddha Carved on Rock in Seosan, there is even Hyeopsi in Bangasang(半跏像) and Bongjiboju(捧持寶珠) type Bosangipsang. In the face of Samjon composition in left-right asymmetry, the unification is indicated while the same line and shape are repeated. Thus, the stably visual balance is being shown. 4. In case of Triad of Buddha Carved on Rock in Seosan, total height in Bonjonbul, left Hyeopsi, and right Hyeopsi was 2.80m, 1.66m, and 1.70m, respectively. Height ratio in left-right Hyeopsibul was 0.60:0.62, thereby having been almost equal. On the other hand, the area ratio was 28.8:25.2, thereby having shown bigger difference. The area ratio on a plane was grasped to come closer to Samjae aesthetic proportion. 5. The axial angle of centering on Gwangbae was 84:46:50, thereby having been close to right angle. On the other hand, the axial angle ratio of centering on Yeonhwajwa(蓮華坐: lotus position) was measured to be 135:25:20, thereby having shown the form of inequilateral triangle close to obtuse angle. Accordingly, the upper part and the lower part of Triad of Buddha Carved on Rock in Susan are taking the stably proportional sense in the middle of maintaining the corresponding relationship through angular proportion of inequilateral triangle in right angle and obtuse angle. 6. The distance ratio in the upper half was 0.51:0.36:0.38. On the other hand, the distance ratio in the lower half was 0.53 : 0.33 : 0.27. Thus, the up-down and left-right symmetrical balance is being formed while showing the image closer to inequilateral triangle. 7. As a result of examining relationship of Samjae-mi(三才美) targeting Triad of Buddha Carved on Rock in Susan, the angular ratio was shown to be more notable that forms the area ratio or triangular form rather than length ratio. The inequilateral triangle, which is formed centering on Gwangbae(光背) in the upper part and Yeonhwajwa(lotus position) in the lower part, is becoming very importantly internal motive of doubling the constructive beauty among Samjae, no less than the mutually height and area ratio in Samjonbul.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.3
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• pp.355-360
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• 2012

In this paper, an stepped-impedance low pass filter(SI-LPF) of triangular-patch type is proposed. A SI-LPF designed according to the standard SI-LPF design procedure is folded as a right angled triangle. The figure of merits of this structure are the adjustabilities of the cut off frequency, the stopband and the attenuation pole frequency of the proposed LPF by varying the resultant slots after folding the SI-LPF compactly for miniaturization. The size of the fabricated LPF is $13.75mm{\times}6.875mm$, which is 24.4 % reduced one compared to that of the conventional SI-LPF. The measured results of the LPF show return loss of less than -10 dB at passband, insertion loss of less than -10 dB at stopband and wide stopband from 3.5 GHz to 10 GHz (about $3f_c$).

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.7
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• pp.768-773
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• 2012

A branch-line hybrid using microstrip artificial transmission lines(ATLs) with slotted-triangular patches is proposed. The proposed artificial transmission line is compact in structure as well as easy to adjust the characteristic impedance and electrical length of equivalent transmission line by changing the slot's parameters; hence, it is useful for miniaturizing conventional transmission lines. The designed branch-line hybrid, because of the use of the right angled isosceles triangular shaped artificial transmission lines as building blocks, has no useless empty space, and hence optimally miniaturized. A fabricated 3 dB branch-line hybrid shows the coupling variation of ${\pm}0.5$ dB and the phase difference between two output ports of $91^{\circ}{\pm}4^{\circ}$ within 15 % bandwidth at 2.45 GHz center frequency. The size of proposed branch-line hybrid is only 38% of the conventional branch-line hybrid.