• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.341-351
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• 2007

The primary purpose of this treatise is to suggest the solutions as follows for the errors concerning the triangle determination and congruence in every Korean mathematics textbook for 7th graders: showing that SsA, along with SSS, SAS, ASA, should also be included as the condition for triangle determination, congruence and similarity; proving that contrary to what has been believed, minimality applies only to congruence and similarity but not to determination; examining related Euclidean propositions; discussing the confusion about the characteristics of determination and congruence; and considering the negative effects of giving definite figures in construction education. The secondary purpose is to analyze the significance of triangle determinant that is not dealt with in either Euclid's Elements or the text books in the U.S. or Japan, and suggest a way to effectively deal with triangle determination and congruence in education.

• 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.

• 월간 기계설비
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• s.224
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• pp.54-63
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• 2009

2009년 개정된 노동법이 발표되었다. 이번 개정에는 ${\triangle}$차별금지 및 사회정책분야 ${\triangle}$산업안전보건 및 산재보험 분야 ${\triangle}$남녀고용평등과 일 가정 양립지원에 관한 법률 벌칙 등이 포함되었다. 본지는 개정된 노동법 중 회원사 인사담당 실무자들이 꼭 알아야 할 내용을 개제한다.

• East Asian mathematical journal
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• v.22 no.1
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• pp.17-35
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• 2006

Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Banach spaces are given. Applications for complex-valued functions are considered as well.

• East Asian mathematical journal
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• v.23 no.1
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• pp.59-73
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• 2007

A new reverse of the generalised triangle inequality that complements the classical results of Diaz and Metcalf is obtained. Applications for inner product spaces and for complex numbers are provided.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.561-573
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• 2023

In this paper, we extend the medial triangle theorem and Varignon's theorem to generic two-dimensional polygons and highlight the role played by diagonals in this process. One of the results is a synthetic definition of the concept of median for an n-sided polygon.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.10
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• pp.2567-2586
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• 2012

Localization of sensor nodes is a key technology in Wireless Sensor Networks(WSNs). Trilateration is an important position determination strategy. To further improve the localization accuracy, a novel Trilateration based on Point In Triangle testing Localization (TPITL)algorithm is proposed in the paper. Unlike the traditional trilateration localization algorithm which randomly selects three neighbor anchors, the proposed TPITL algorithm selects three special neighbor anchors of the unknown node for trilateration. The three anchors construct the smallest anchor triangle which encloses the unknown node. To choose the optimized anchors, we propose Point In Triangle testing based on Distance(PITD) method, which applies the estimated distances for trilateration to reduce the PIT testing errors. Simulation results show that the PIT testing errors of PITD are much lower than Approximation PIT(APIT) method and the proposed TPITL algorithm significantly improves the localization accuracy.

• 월간 기계설비
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• s.241
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• pp.34-37
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• 2010

공정거래위원회가 지난해 말 20개 건설업체를 대상으로 하도급 현장조사를 실시한 결과 조사대상 업체 모두 법위반 행위를 하고 있음을 적발, 약 4억원의 과징금 부과와 총 51억원 상당의 위반금액을 936개 관련 하도급업체들에게 지급하도록 조치했다. 확인된 법위반 유형으로는 $\triangle$부당하게 하도급대금 결정 $\triangle$하도급대금 지연이자 미지급 $\triangle$어음할인료 수수료 미지급 $\triangle$선급금 지급 위반 $\triangle$지급보증 불이행 등이 대부분이다. 특히, 하도급공사 입찰시 입찰최저가가 이미 자기 실행예산보다 낮음에도 불구하고 이보다 더 낮추기 위해 금지되어 있는 재입찰 방식이나 추가 인하 수단을 동원한 바 있고, 자기 회사는 공공기관 등 발주자로부터 현금으로 공사대금을 받고도 하도급업체들에게는 현금이 아닌 장기어음 등으로 지급하는 등의 사례가 적발됨으로써 나쁜 관행이 여전히 만연되고 있는 것으로 나타났다.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• 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.