• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.393-407
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• 2009

In this article the definition of similarity and its introduction in Korean middle school textbooks based on the 7th national curriculum are analysed critically. As a result four suggestions are presented. First, on the consideration that the contents related with similarity has been removed in the elementary school curriculum, the meaning of 'constant rate' needs to be understood through the rich experience of drawing enlarged/reduced figures when similarity is introduced in middle school, Second, there are two different ways in enlargement/reduction of figures and in the definition of similarity. Teachers have to keep the limitations of the two ways in mind. Third, the activity of drawing similar figures in enlarged/reduced squared paper needs to be practiced. Last, on 'the relation of similarity' which is in the definition of similarity, it has to be examined whether 'similarity' should be presented in the documents of the national curriculum as a term.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2020.07a
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• pp.236-238
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• 2020

기존에 개발한 삼각형 닮음 조건 기반 영상 간 유사 공간 계산 알고리즘은 근접 거리에 과도하게 많은 특징점이 추출되면 정확도가 낮아지는 점, 계산 과정에서의 Threshold를 주관적으로 설정해 주어야 해 정확한 Threshold를 찾기 위하여 전체 알고리즘을 여러번 반복하여 실행시켜야 하는 점에서 비효율적인 측면이 있다. 이를 해결하기 위하여 본 논문에서는 기존의 삼각형 닮음 조건 기반 영상 간 유사 공간 계산 알고리즘에 근접 거리 내의 특징점을 제거하는 알고리즘과 서로 다른 Threshold를 가진 유사 공간 계산 알고리즘들을 병렬적으로 계산해 한 번의 알고리즘 실행만으로 자동적으로 적절한 Threshold를 찾을 수 있도록 하는 모듈을 추가하여 기존의 알고리즘과 비교하여 더 효율적으로 영상 간 유사 공간을 계산해낼 수 있도록 개선된 삼각형 닮음 조건 기반 영상 간 유사 공간 계산 알고리즘을 제안한다.

• Journal of the Korean School Mathematics Society
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• v.26 no.2
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• pp.111-135
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• 2023

This study conducted a student-centered inquiry lesson on the similarity of figures using AlgeoMath, with student learning aspects analyzed from a communication perspective. This approach aimed to inform pedagogical implications related to teaching geometric similarity. Through utilizing AlgeoMath, students were able to visually confirm that their chosen figures were similar, experiencing key mathematical concepts such as the ratio of similarity to the area of similar figures, and congruency and similarity conditions of triangles. In the lessons applying this concept, we categorized the features of similarity learning displayed by students, as seen in the communication aspects of their exploratory activities, into 'Understanding similarity ratios', 'Grasping conditions of similarity in triangles', and 'Comparing concepts of congruency and similarity'. Through exploratory activities based on AlgeoMath, students discussed the meaning and mathematical relationships of key concepts related to similarity, such as the ratio of similarity to the area of figures, and the meaning and conditions of congruence and similarity in triangles. By improving misconceptions about the similarity of figures, they were able to develop deeper mathematical understanding. This study revealed that in teaching and learning the geometric similarity using AlgeoMath, obtaining meaningful pedagogical outcome was not solely due to the features of the AlgeoMath environment, but also largely depended on the teacher's guidance and intervention that stimulated students' thinking.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.1-24
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• 2009

The applications of ratio and similarity have been in need of everyday life from ancient times. Euclid's elements Ⅴand Ⅵ cover ratio and similarity respectively. In this note, we have done a comparative analysis to button down the contents of ratio and similarity covered by the math text books used in Korea, Euclid's elements and the math text books used in Japan and America. As results, we can observe some differences between them. When math text books used in Korea introduce ratio, they presented it by showing examples unlike math text books used in America and Japan which present ratio by explaining the definition of it. In addition, in the text books used in Korea and Japan, the order of dealing with condition of similarity of triangles and the triangle proportionality is different from that of the text books used in America. Also, condition of similarity of triangles is used intuitively as postulate without any definition in text books used in Korea and Japan which is different from America's. The manner of teaching depending on the way of introducing learning contents and the order of presenting them can have great influence on student's understanding and application of the learning contents. For more desirable teaching in math it is better to provide text books dealing with various learning contents which consider student's diverse abilities rather than using current text books offering learning contents which are applied uniformly.

• Proceedings of the KAIS Fall Conference
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• 2009.12a
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• pp.626-629
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• 2009

본 논문에서는 MPEG2(Moving Picture Expert Group 2)비디오 디코더에서 영상데이타를 디코딩하는 기술에 관한 것으로, 종래의 동여상 처리기에서는 허프만 코드화 처리를 하여 정지영상을 부호화한 후 분할기반 부호화 방식의 동영상 처리기법을 사용하였으나 1프레임의 코드화시에도 많은 계산 알고리즘이 필요하고 이미지의 닮음정도를 객관적수치로 표현할 수 없으므로 비슷한 이미지를 중복 코드화 작업 및 전송 작업을 하는 결함이 있었다. 본 눈문에서는 이를 해결하기 위하여 이미지의 닮음정도를 수치화하고 기준값 이하의 영상은 코드화 작업을 하지않고 계산된 영상 변화값에 의해 구현된 영상으로 대체하여 저장 및 전송하도록 하여 시각적으로 전혀 거부감이 없는 동영상을 구현하였다.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.469-482
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• 2006

It ill give much interest both to the teacher and student that paper crane makes interesting mathematical investment possible. It is really possible for the middle school students to invest mathematical activity such as the things about triangle and square, resemblance, Pythagorean theorem. I reserched how this mathematical investment possible through folding and unfolding paper crane and analyzed the mathematical meaning.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2019.06a
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• pp.313-316
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• 2019

IT기술의 발전으로 다양한 디바이스들이 출현하고 있고, 디바이스들의 디스플레이 크기와 해상도가 증가하는 경향을 보임에 따라 파노라마 영상에 대한 필요성이 대두되고 있다. 현 상황에서 영상 소비 목적과 사용 디바이스에 맞는 영상을 제공하기 위하여 불특정 해상도를 가진 영상들을 정합하여 파노라마 영상을 제작하는 것이 필수적이다. 이와 같은 파노라마 영상을 제작하기 위해서는 영상 간 스티칭 기술이 필요하며, 해당 스티칭 기술은 영상 전체에 대한 정보를 사용하기 때문에 많은 시간이 소요된다. 이러한 문제점을 해결하기 위하여, 스티칭 대상 영역을 특정하는 영상 간 공간유사도 평가를 활용하면 스티칭 시간의 감소를 가져올 수 있다. 본 논문에서는 추출된 특징점을 대상으로 삼각형 닮음 조건을 적용하여 영상 간 공간유사도를 평가하는 알고리즘을 개발하고자 한다.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.4
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• pp.187-194
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• 2011

In this paper, JPEG(Joint Photographic Experts Group) image data video decoding technique is presented, it is Huffman decoding method and fractal image method which is very complexive algorithm and the time required much it to implement this method and the first image is decoded to video frame image. This have defect of overlap decoding and transport work because of impossible to represent objective value of resemblance. The proposed method was calculated the mathematical absolute image resemblance and simplify the moving picture process to reducing the step of moving picture codefying. The results show that smoothed moving picture compared recent methods.