环形珠垫编织的数学模型  

Mathematical model of the weaving of ring bead pads

作　　者：吕晓静[1] 吴琼 屈非非[1] Lü Xiao-jing;WU Qiong;QU Fei-fei(School of Science,Tianjin University of Technology and Education,Tianjin 300222,China)

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《高师理科学刊》2018年第11期1-4,共4页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(11601391);天津职业技术师范大学出国研修资助项目(J10011060318);天津职业技术师范大学教学改革与质量建设研究重点项目(JGZ2015-08)

摘　　要：分析目前比较流行的环形珠垫手工编织方法,将编织的方法用周期运动的数学形式予以表示,建立笛卡尔直角坐标系,给出编织运动路径的坐标表达式.借助数学软件实现了编织路径运动的仿真.对成品珠垫采用纵向和环形2个不同角度的分析,发现了串珠排列的几何规律——杨辉三角形和等差数列,利用几何特征确定环形珠垫珠子总数与编织圈数以及珠垫面积之间的数量关系.The method of weaving ring bead pads by hand is analyzed,the method of knitting is expressed in the mathematics form of periodic motion.The Cartesian coordinate system is established and the coordinate expression of weaving motion path is given.The simulation of weaving path movement is realized by means of mathematical software.Through the analysis of the finished bead pads with two different angles,longitudinal and annular,finds the geometric regularities of the bead arrangement--Pascal Triangle and equal difference series.The relationship between the total number of beads and the number of braided loops and the area of the beads is found by using of geometric features.

关 键 词：环形编织 杨辉三角 几何计算 

分 类 号：O29[理学—应用数学] TH122[理学—数学]