폴리오미노와 채색도형에 대한 연구

문정현,백기현,최준호,김선정,황혜정,문희진 한국과학영재교육학회 2017 과학영재교육 Vol.9 No.3

A polyomino is a plane geometric figure formed by joining several unit squares edge to edge. The main research content of the paper is to calculate the number of colored polyomino. That is, we calculate the number of all cases when two adjacent rectangles are colored so that they do not have the same color by using colors for polyomino composed of unit squares for given natural numbers and . 폴리오미노는 여러 개의 단위 정사각형의 변들을 이어 붙여서 평면도형을 의미한다. 본 논문의 주요 연구 내용은 채색된 폴리오미노의 개수를 계산하는 것이다. 즉, 주어진 자연수 과 에 대해, 개의 단위 사각형으로 이루어진 폴리오미노에, 가지의 색을 이용하여 인접한 두 사각형이 같은 색이 되지 않도록 채색할 때 나타날 수 있는 모든 경우의 수를 계산하는 것이다

3차원 서페이스에 대한 폴리오미노 타일링

조청운(Cheung Woon Jho) 한국컴퓨터게임학회 2013 한국컴퓨터게임학회논문지 Vol.26 No.4

This paper presents a new polyomino tiling algorithm for three-dimensional surface geometric model. We first apply surface subdivision to the input polygonal mesh or subdivision surface mesh. Then we construct a random Hamiltonian path to connect all subdivided input mesh. This path is used to build initial polyomino tiling on the original input mesh. Finally we apply random polyomino exchanging to the polyomino tiling to get more uniform occurrence of each polyomino types. Our method is applicable to construct three-dimensional puzzle and we show the results of proposed algorithm on three-dimensional mesh data.

Undecidability of tiling the plane with a set of 5 polyominoes

김윤후 대한수학회 2026 대한수학회지 Vol.63 No.2

In this paper, we give a proof that it is undecidable whether a set of five polyominoes can tile the plane by translation. The proof involves a new method of labeling the edges of polyominoes, making it possible to assign whether two edges can match for any set of two edges chosen. This is achieved by dedicating 1 polyomino to the labeling process.

폴리오미노에 What if (not)? 전략을 적용한 영재 학급용 수학 수업 소재 발굴과 활용

구본왕,송상헌 대한수학교육학회 2011 학교수학 Vol.13 No.1

본 연구는 폴리오미노에 What if (not)?이라는 기법을 적용하여 영재학급용 수학 수업 소재를 발굴하고 이를 수업에 활용한 사례 분석을 통해 수학영재교육의 시사점을 도출하고자 한다. 이를 위해 학생들이 흔히 접할 수 있는 블로커스라는 게임을 사용하여 폴리오미노의 특징을 이해하도록 구성하였고, 한중일 동양 3국의 전통적인 두뇌스포츠인 오목이라는 게임을 접목한 탐구 활동을 개발하였다. 블로커스 오목이라는 새로운 소재에 Pick의 정리를 적용하면서, 블로커스 오목 활동을 하는 동안 창의적인 학습이 되도록 구성하였다. 본 연구는 수학 수업 소재를 발굴 및 활용하여 학생들에게서 나타나는 각 소재별 특징과 결과를 바탕으로 최종적인 수업 소재를 제안하였다. 이를 통해 초등학교 수학영재 학생과 교사들을 위한 5가지 시사점을 얻을 수 있었다. The purpose of this study is to develop and utilize various kinds of mathematics teaching materials for gifted class in elementary school by utilizing polyominoes and a what-if-not strategy. Blokus is used to let students understand the characteristics of polyominoes, and omok is utilized to let them grasp interior point. Thus, the activities that utilized the new materials, blokus and omok, are developed to teach Pick's theorem. Besides, recreation activities were additionally prepared to provide education in an easy, intriguing and creative manner. The findings of the study is as follows:First, each of the materials was utilized in a different manner when the students engaged in basic and enrichment learning. Second, the mathematically gifted students were able to discover Pick's theorem in the course of utilizing the materials that contained recreational elements. Third, the students were taught to foster their problem-solving skills about area, girth and interior point by making use of the materials that were designed to be linked to each other. Fourth, existing programs were just designed to attain particular objects, to be conducted at a fixed time and to cater to particular graders. Fifth, when the students made problems by making use of the what if (not) strategy and the materials, they responded in diverse ways and were able to apply them.

수학 영재 교수·학습 자료 개발을 위한 소재 발굴에 관한 연구

송상헌 仁川敎育大學校 科學敎育硏究所 2004 과학교육논총 Vol.16 No.-

영재들을 위한 수학 교수·학습용 자료를 개발하는 일은 지속적이면서도 장기적인 과제이다. 자료 개발을 위해서는 참신한 소재를 발굴하는 일부터 선행되어야 한다. 이 글은 초등학교 5-6학년 정도의 수준에 해당하는 수학 영재들에게 적용해 볼 수 있는 교수·학습용 자료 개발의 소재를 발굴한 사례를 담고 있다. 손 조작교구 퍼즐 교구(탱그램과 폴리오미노)라는 재료적인 측면과 "what if ~? 또는 what if not~?"이라는 기법이라는 발문과 안내된 재발명이라는 교수방법적인 측면을 활용하여 영재 교수·학습용 자료개발을 위해 퍼즐의 발생과정을 재구성해 보았다. 이는 도형과 측정영역의 내용 통합적인 측면에서 주제탐구형의 교수-학습 자료 개발을 위한 좋은 소재가 될 것이다. This study is on the investigating topics to develop teaching/learning materials for the mathematically gifted child. I constructed the handling teaching material tools(jigsaw tangram, and polyominoes) according to their genetic process, and reconstructed by the "what if -? / what if not~?" strategy This study will be a good topics for the development of teaching/learning materials for the mathematically gifted child, especially 5-6 grades students.

균일 분포 테트로미노 타일링

조청운 한국컴퓨터게임학회 2013 한국컴퓨터게임학회논문지 Vol.26 No.3

TILINGS OF ORTHOGONAL POLYGONS WITH SIMILAR RECTANGLES OR TRIANGLES

SU, ZHANJUN,DING, REN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1

In this paper we prove two results about tilings of orthogonal polygons. (1) P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. An orthogonal polygon P can be tiled with similar copies of R(u) if and only if u i algebraic and the real part of each of its conjugates is positive; (2) Laczkovich proved that if a triangle $\Delta$ tiles a rectangle then either $\Delta$ is a right triangle or the angles of $\Delta$ are rational multiples of $\pi$. We generalize the result of Laczkovich to orthogonal polygons.

A House Design Method of Normative Modules adopting Hanok and Traditional Building Framing Skills

Soo-Hoon Park 한국멀티미디어학회 2018 멀티미디어학회논문지 Vol.21 No.3

A House Design Method of Normative Modules adopting Hanok and Traditional Building Framing Skills

Park, Soo-Hoon Korea Multimedia Society 2018 멀티미디어학회논문지 Vol.21 No.3

In this paper, we try to verify a normative module based house design procedure consisted of several sequential steps. The first step is to suggest formalization of designing so that we could clarify each phase and operation we are adopting in our design process. The second step is the clearing up the conceptual schema of traditional skills that we adopt and utilize from traditional Hanok framing techniques. The third step is to formulate adequate modular kits for the assembly of house design solutions for the schematic, conceptual and preliminary phases of designing. The fourth step is to implementing our ideas and methods to a proper computational platform such as Unity3D. The final step is to verify our symbolic descriptions of design formalization with the output of our experiments so that we have better understanding of design reasoning characteristics such as in house design.

프랙타일의 경계부분에 대한 프랙탈 차원

Kang, Byung-Sik 고신대학교 자연과학연구소 1999 고신대학교 자연과학연구소 논문집 Vol.9 No.-

The radix representation for number systems shows a fractal structure. The complex number system yields some tiles whose boundaries are fractal curves in the complex plane. The fractal code of their iterated function system of the fractiles can be generalized the inverse of an integral matrix as a contraction. There are three affine types of fractiles homeomorphic to a disk with two pieces, and seven types with three pieces from the expensive matrices. Moreover 29 four piece fractiles are derived from tetrominos. We calculate the fractal dimension of the boundary of 29 fractiles in this paper.