• Communications of Mathematical Education
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• v.38 no.2
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• pp.215-230
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• 2024

Congruences and symmetry are familiar concepts that can be encountered in everyday life. In order to effectively understand and acquire these concepts, the role of appropriate visual examples is important. This analysis examined various visual examples used in the process of learning the concepts of congruence and symmetry in elementary mathematics textbooks and focused on the use of convex polygons and concave polygons. As a result of the analysis, various types of polygons were used as visual examples for teaching and learning of congruence and symmetry in textbooks. The frequency of use of concave polygons was higher in the order of congruence, line symmetry, and point symmetry, and it was confirmed that it was used more frequently in the process of exploring properties than in the introduction of the concept. Based on these results, a plan to utilize concave polygons in teaching and learning of congruence and symmetry was sought.

• The KIPS Transactions:PartA
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• v.15A no.5
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• pp.295-300
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• 2008

In this paper, we consider a characterization of a Guard Sufficiency Set(GSS) in the hierarchy of simple polygons. we propose the diagonals of a arbitrary triangulation of a polygon as a GSS when guards see the diagonals with completely visibility and both sides of the diagonal. we show that this can be a GSS in convex polygons, unimodal polygons, spiral polygons but this can not be a GSS in star-shaped polygons, monotone polygons, completely external visible polygons.

• Transactions of Materials Processing
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• v.11 no.5
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• pp.405-413
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• 2002

A process planning system for cold forging of non-axisymmetric parts of comparatively simple shape was developed in this study. Programs for the system have been written with Visual LISP in AutoCAD. Shape of the product must be drawn with the solid line and the hidden line, and with the plane and front view, as well. At the plane, the system recognizes the external shape of non-axisymmetric portions - the number of the sides of the regular polygons and the radii of circles inscribing and circumscribing the polygon. At the front view, the system cognizes the diameter of axisymmetric portions and the height of the primitive geometries such as polygon, cylinder, cone, concave, convex, etc. The system perceives that the list developed from the solid line must be formed by the operation of forward extrusion or upsetting, and that the list developed from the hidden line must be formed by the operation of backward extrusion. The system designs the intermediate geometries again by considering clearance between workpiece and die, and then finally the billet diameter, in reverse order from the finished product, on the basis of volume constancy and using the operations, the forming sequence, the number of operations and the intermediate geometries which were already designed. The design rules and knowledges for the system were extracted from the plasticity theories, handbook, relevant reference and empirical knowledge of field experts. Suitability of the process planning was analyzed using SuperForge of FVM simulation package. The results of analysis showed good formability.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.335-352
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• 2005

In this paper, we consider a center of gravity of convex polygon which could be an enriched topic for the gifted in mathematics(7th grades) and suggested a case that the gifted experienced a center of gravity. Based on properties of Archimedes' center of mass, we define it as a point which make a polygon be in counterpoised with its area and explain how to find that point through using integral calculus or internal division. Then we consider that the gifted would experience various kinds of mathematical thinking and apply diverse ways of problem solving 3s searching for this topic. As this research, the teacher would be able to conduct the gifted with penetration into center of gravity and to let them participate in advanced learning courses which value ma-thematical thinking while they undergo similar experiences such as mathematicians.

• Korean Journal of Environment and Ecology
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• v.26 no.2
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• pp.186-191
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• 2012

The Chinese Sparrowhawk($Accipiter$ $soloensis$) is the most common breeding raptor in Korea, but its spatial use in the breeding season has been poorly documented. Therefore, to estimate the territory and home range sizes of breeding sparrowhawks, six territorial males(four in 2005 and two in 2006) were observed from June to July in Gyeonggi Province, the Republic of Korea. Main perches, which were used repeatedly(more than three times) or where apparent territorial behaviors were observed, were identified and the locations were analyzed by GIS software. According to the 100% Minimum Convex Polygons which were identified from $25.2{\pm}5.3$ perches, Chinese Sparrowhawks occupied $4.62{\pm}0.90$ ha for breeding territories and used $22.57{\pm}5.12$ ha for their home ranges. These estimates showed larger spatially occupied areas than those in one previous report, but this study suggests that Chinese Sparrowhawks intensively use small areas throughout the breeding season. This result also implies that the sparrowhawks have the potential to be significantly affected by any habitat changes and resource exploitation in the small areas(particularly in small rice paddies of 0.6-2.0 ha) which they largely rely on for food. Although this study was based on observations solely for territory size estimations, this study may be worthwhile as preliminary pilot research for Chinese Sparrowhawk conservation, management, and further studies.

• Journal of Gifted/Talented Education
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• v.27 no.1
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• pp.37-57
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• 2017

In terms of making more various geometrical figures than existing Tangram, Sphinx Puzzle has been used as a material for the gifted education. The main research subject of this paper is to verify how many convex polygons can be made by all pieces of a Sphinx Puzzle. There are several previous researches which dealt with this research subject, but they did not account for the clear reasons on the elementary level. In this thesis, I suggest using unit area and minimum area which can be proved on the elementary levels to account for this research subject. Also, I composed the program for the mathematically gifted elementary students, regarding the subject. I figured out whether they can make the mathematical justifications. I applied this program for three 6th grade students who are in the gifted class of the G district office of education. As a consequence, I found that it is possible for some mathematically gifted elementary students to justify that the number of convex polygons that can be made by a Sphinx Puzzle is at best 27 on elementary level.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.589-608
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• 2015

The inquiry subject of this paper is the number of convex polygons one can form by attaching the seven pieces of a tangram. This was identified by two mathematical proofs. One is by using Pick's Theorem and the other is 和々草's method, but they are difficult for elementary students because they are part of the middle school curriculum. This paper suggests new methods, by using unit area and the minimum area which can be applied at the elementary level. Development of programs for the mathematically gifted elementary students can be composed of 4 class times to see if they can prove it by using new methods. Five mathematically gifted 5th grade students, who belonged to the gifted class in an elementary school participated in this program. The research results showed that the students can justify the number of convex polygons by attaching edgewise seven pieces of tangrams.

• Korean Journal of Computational Design and Engineering
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• v.4 no.3
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• pp.190-199
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• 1999

Presented in this paper is an algorithm for finding all intersections among polygonal chains with an O((n+k)·log m) worst-case time complexity, where n is the number of lien segments in the polygonal chains, k is the number of intersections, and m is the number of monotone chains. The proposed algorithm is based on the sweep line algorithm. Unlike the previous polygonal-chain intersection algorithms that are designed to handle special only cases, such as convex polygons or C-oriented polygons, the proposed algorithm can handle arbitrarily shaped polygonal chains having self-intersections and singularities (tangential contact, multiple intersections). The algorithms has been implemented and applied to 1) testing simplicity of a polygon, 2) finding intersections among polygons and 3) offsetting planar point-sequence curves.

• Korean Journal of Computational Design and Engineering
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• v.2 no.3
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• pp.186-194
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• 1997

This paper describes new methods to minimize the cutting time in zigzag milling operation of two dimensional polygonal surfaces. Previous works have been focused on mainly experimental approaches by considering some machining parameters such as, spindle speed, depth of cut, cutter traverse rate, cutter diameter, number of teeth, tool wear, life of tool, and so on. However, in this study, we considered two geometrical factors one by one in order to see the effect separately, which are the length of cut and the number of cutter traverse. In an N-sided concave or convex polygon, an algorithm has been developed which minimize the total length of cut. Also, a heuristic approach was used to minimize the number of cutter traverse.

• Journal of information and communication convergence engineering
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• v.9 no.1
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• pp.105-109
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• 2011

In this paper, we study the dominating-free sest which is defined as follows: k points called servers and n points called clients in the plane are given. For a point p in the plane is said to be dominated by a client c if for every server s, the distance between s and p is greater than the distance between s and c. The dominating-free set is the set of points in the plane which aren't dominated by any client. We present an O(nklogk+$n^2k$) time algorithm for computing the dominating-free set under the $L_1$-metric. Specially, we present an O(nlogn) time algorithm for the problem when k=2. The algorithm uses some variables and 1-dimensional arrays as its principle data structures, so it is easy to implement and runs fast.