• Proceedings of the Korean Society of Computer Information Conference
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• 2011.06a
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• pp.315-316
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• 2011

수학 함수 중에서 삼각함수는 그 활용도가 매우 높아서 아주 많이 사용되는 함수 중 하나이다. 직각 삼각형의 직각이 아닌 한 각의 크기를 a라 하면, 이 삼각형의 임의의 두 변의 길이의 비는 이 각 a의 크기에 의하여 결정되므로 이 비를 이각의 삼각 함수라 하였다. 즉, 삼각함수는 직각삼각형에서 한 각의 크기가 일정하면, 이들 변의 비의 값은 삼각형의 크기에는 관계없이 일정하다는 가장 단순하고 독특한 성질에 기초를 둔 학문이다. 어떠한 대상체의 높이는 직삼각형의 밑변의 길이와 건물을 올려다본 각이 있다면 삼각함수를 이용하여 쉽게 구할 수 있다.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.25-38
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• 2005

We briefly survey the history of Chinese mathematics which concerns the resolution of right triangles. And we analyse the problems Yucigugosulyodohae(劉氏勾股述要圖解) which is the mathematical book of Chosun Dynasty and contains the 224 problems about right triangles only. Among them, 210 problems are for resolution of right triangles. We also present the methods for generating the Pythagorean triples and constructing polynomial equations in Yucigugosulyodohae which are needed for resolving right triangles.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.41-52
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• 2009

This study investigates a mathematical subject, 'triangles' in mathematics books of Chosun Dynasty, in special Muk Sa Jib San Bub(默思集算法), Gu Il Jib(九一集), San Hak Ib Mun(算學入門), Ju Hae Su Yong(籌解需用), and San Sul Gwan Gyun(算術管見). It is likely that they apt to avoid manipulating general triangles except the right triangles and the isosceles triangles etc. Our investigation says that the progress of triangle-related contents in Chosun mathematics can fall into three stages: measurement of the triangle-shaped fields, transition from the object of measurement to the object of geometrical study, and examination of definition, properties and validation influenced by western mathematics.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.7
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• pp.709-720
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• 2014

In this paper, we studied miniaturization of LPDA(Log-Periodic Dipole Array) antenna used for VHF and UHF bands. To miniaturize the LPDA antenna, in this study, the radiation elements in a low frequency were changed into a triangular meander structure which has small current cancelation effect at feed part. For the triangular meander structure, an isosceles triangular and right triangular meander structures were proposed and the LPDA antennas were miniaturized by using the two meander structures. Also, the simulated and measured results were compared for the two miniaturized LPDA antennas. As a result, the isosceles triangular meander and right angle triangular meander structure applied LPDA antennas were reduced up to 60.5 % and 72.4 % compared a basic LPDA antenna, respectively. Consequently, we confirmed that the triangular meander structure is suitable for miniaturization of a LPDA antenna.

• Journal of Advanced Navigation Technology
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• v.26 no.5
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• pp.344-349
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• 2022

A compact LPDA antenna consisting of right triangle-shaped dipole elements appended with strips is proposed for UWB applications. First, right triangle-shaped dipole elements are used instead of conventional strip dipole elements to reduce the width of the LPDA antenna. Second, the spacing between the LPDA elements is decreased to reduce the length of the LPDA antenna. Finally, strips are appended at the ends of the right triangle-shaped dipole elements in order to further reduce the width of the antenna. A prototype of the proposed antenna with 16 elements and gain > 4 dBi is fabricated on an FR4 substrate with dimensions of 44 mm×30 mm. Measured frequency band of the fabricated antenna is 2.99-14.76 GHz for a VSWR < 2, which ensures UWB operation, and measured gain range is 4.0-5.5 dBi with a front-to-back ratio larger than 10 dB. The length and width of the proposed compact LPDA antenna are reduced by 40.9% and 20.6%, respectively, compared to the conventional LPDA.

• Education of Primary School Mathematics
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• v.20 no.4
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• pp.305-319
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• 2017

In the process of finding the triangle height, 26 students in the 6th grade were surveyed to understand the students' triangle height through the eye movement data and to investigate the cognitive load of the students. As a result, the correctness rate of the pre-test was significantly increased in the post-test, and the frequency and retention of gaze data were smaller in the post-test than in the AOI of each question. The Participants's subjective cognitive load indicated that it was more difficult to understand the concept of rotated triangles compared with upright triangles that were parallel to the ground. More frequent and more retentions in the eye-tracking data were detected in the right triangles and acute triangles by rotating configuration. Eye movement data show that eye tracking technology can provide an objective measure of students' cognitive load for feedback on instructional design.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.51-62
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• 2008

In the 7th-curriculum, only basic arithmetics of complex numbers have been taught. They are taught formally like literal manipulations. This paper analyzes mathematically essential relations between algebra of complex numbers and plane geometry. Historical analysis is also performed to find effective methods of teaching complex numbers in school mathematics. As a result, we can integrates this analysis with school mathematics by help of Viete's operations on right triangles. We conclude that teaching geometric interpretation of complex numbers is possible in school mathematics.

• Journal for History of Mathematics
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• v.33 no.3
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.5-6
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• 2010

In this study, assuming that there is a diagonal uniaxial compression field in combination with triangular homogeneous stress fields in the cracked concrete wall and a tensile stress of a steel plate occurs in the perpendicular to the direction of the diagonal compression field, an ultimate shear strength of a slender composite shear wall is estimated.