• 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 of Educational Research in Mathematics
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• v.27 no.3
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• pp.431-449
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• 2017

Acute triangles and obtuse triangles are defined according to the classification of triangles by angles. The definitions of acute triangles and obtuse triangles are difficult for students because they are related to different logical elements. The purpose of this study is to seek desirable methods for teaching the classification of triangles by angles related to logic. To do this, based on the theoretical consideration and the longitudinal analysis of the elementary mathematics textbooks, some implications are found for teaching. And then the lesson was planned and applied to $4^{th}$ graders. After the lesson, we reviewed and analyzed their worksheets and test results for examining the effects by teaching methods. Based on the result, we discussed and made some didactical suggestions for teaching the classification of triangles by angles.

• The Mathematical Education
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• v.41 no.2
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• pp.203-213
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• 2002

In this paper, we introduce the concepts of geometric and arithmetic triangles. Geometric and arithmetic triangles are special types of rational Heron triangles - triangles with rational sides and area. In addition, the theory illustrated in this paper gives certain theorems on the determination of non-right angled geometric and arithmetic triangles. In the meantime, with the help of Mathematica, we compute the sides and area of several triangles(GRT, IGT, RIGT, RAT). Since the material presented in this paper is within the reach of undergraduates, it can attract attention of mathematics students and may also be of interest to the mathematicians. In this content we believe this paper can help undergraduates to have interests in the new world of mathematics.

• Research in Mathematical Education
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• v.15 no.4
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• pp.327-340
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• 2011

In this paper we propose an inquiry task on the subject of congruent triangles. The task deals with conditions that are sufficient for congruency, and conditions that are insufficient. The aim of the task is to find the minimal number of identical components in two triangles that is sufficient to ensure congruency.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1597-1617
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• 2017

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely many non-similar integer Sharygin triangles.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.89-100
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• 2005

This study is to compare contents of mathematics textbooks of Korea and Russia laying stress on topic 'congruence of triangles'. We analyze and compare contents description system, relation between congruent conditions of triangles and construction problem, and jestification methods of congruent conditions of triangles in Korean and Russian mathematics textbooks.

• 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.

• Wind and Structures
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• v.15 no.4
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• pp.345-354
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• 2012

This work discusses the wind stability requirements specified by UN Reg. 27 on emergency car warning triangles, which are of mandatory use in many countries. Wind tunnel experiments have been carried out in order to determine aerodynamic coefficients of commercial warning triangles and the friction coefficients between the triangle legs and an asphalt base that fulfils the roughness requirements stated by Reg. 27 for wind stability certification. The wind stability specifications for warning triangles are reviewed, compared with pressure field measurements and discussed. Results of wind tunnel tests and comparison with field measurements reported in the literature show that the requirements could be excessively conservative.

• 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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.3
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• pp.35-41
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• 1999

STL which is used in Rapid Prototyping is composed of a lot of triangular facets. The number of triangles and the shapes of these triangles determine the quality of STL. Therefore, proper algorithm is necessary to enhance the quality of triangular patch. In this paper we used the Delaunay triangulation method to apply to following processes. 1) On processing for reducing sharp triangles which cause errors on intersection. 2) On processing for connecting two or more collinear edges. 3) On processing for deleting unnecessarily inserted points in coplanar polygon.