• Journal of ILASS-Korea
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• v.13 no.1
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• pp.9-15
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• 2008

This experimental study was carried out to examine the heat transfer characteristics of impinging air jet on a flat plate with a set of right angled triangle rods. Each right angled triangle rod in the array was positioned normal to the flow direction and parallel to the flat plate surface. The clearances from a right angled triangle rod to flat plate surface (C=1, 2 and 4 mm) and the distance from nozzle exit to flat plate (H=100 and 500 mm) were changed for the pitch between each right angled triangle rods (P=40 mm). As a result, heat transfer shows best performance at the clearance of C=1 mm, in case clearance changed, and the average heat transfer enhancement rate increased up to 47% compared to the result of a flat plate without a right angled triangle rod.

• 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.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.433-444
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• 2024

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

• 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.

• International Journal of Highway Engineering
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• v.16 no.2
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• pp.99-106
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• 2014

PURPOSES : This study is to develop Right-Turning Channelization Design Models of Semitrailer at Intersections by regression of vehicle tracking simulation. METHODS : Based on the literature review, it was indicated that right-turning channelization design guide of semitrailer is too complex and is not reflected turning speed and approach angle. To verify effectiveness of right turning semitrailer trajectories according to the changing turning speed and approach angle, vehicle tracking simulation was executed. And then, simulation results were analyzed for modeling design elements; minimum turning radius, swept path width, arc length, width of triangle island, of right-turning channelization using regression methods. RESULTS : When the turning speed is getting higher, minimum turning radius, arc length, width of triangle island increased and the approach angle lower, swept path width, arc length, width of triangle island reduced. The turning radius completely reflected by turning speed. CONCLUSIONS : In this research, it was investigated how much design elements are changed according to the turning speed and the approach angle of semitrailer. The developed right-turning channelization design models can help engineers to easy and comfortable design at various conditions.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.543-552
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• 2007

We consider estimation of the right-tail probability in a half-triangle distribution, and also consider inference on reliability, and derive the k-th moment of ratio of two independent half-triangle distributions with different supports. As we define a skew-symmetric random variable from a symmetric triangle distribution about origin, we derive its k-th moment.

• East Asian mathematical journal
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• v.31 no.4
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• pp.459-481
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• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• Journal for History of Mathematics
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• v.32 no.4
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• The Mathematical Education
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• v.41 no.2
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• pp.227-231
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• 2002

The Pythagorean theorem and Pythagorean triple are well known. We know some Pythagorean triples, however we don't Cow well that every natural number can belong to some Pythagorean triple. In this paper, we show that every natural number, which is not less than 2, can be a length of a leg(a side opposite the acute angle in a right triangle) in some right triangle, and list some Pythagorean triples.