基于对称群思想的新疆伊斯兰几何纹饰分析

发布时间：2018-04-14 23:24

本文选题：新疆 + 伊斯兰教　；参考：《湖北民族学院学报(哲学社会科学版)》2017年02期

【摘要】：伊斯兰文明关于几何纹饰与对称的创造性使用起始于10世纪,到14世纪时有了令世界瞩目的成就。伊斯兰教在10世纪(明代)传入新疆之后,几何纹饰也在本地区的清真寺、民居、传统工艺品等的装饰上得到传承和创新性的应用。二维连续的重复繁衍的新疆伊斯兰几何纹饰凸显了几何、图样与对称,阐释了无限性及无所不在的宗教教义。文章基于对称、对称变换和对称群的思想,分析了用于定义几何纹饰背后网状系统的五种形态的网格以及二维连续图案的十七种对称群类型,基于平移、旋转、镜射、滑动镜射等对称变换分析了伊斯兰几何纹饰的构图规律,并结合实物图片进行了例证。
[Abstract]:The creative use of geometric ornamentation and symmetry in Islamic civilization began in the tenth century and achieved remarkable achievements in the 14th century.After Islam was introduced into Xinjiang in the 10th century (Ming Dynasty), geometric ornaments were also inherited and innovatively applied in the decoration of mosques, houses and traditional handicrafts in the region.The two dimensional repeated reproduction of Xinjiang Islamic geometric patterns highlights geometry, design and symmetry, and explains the infinite and omnipresent religious doctrine.Based on the ideas of symmetry, symmetry transformation and symmetric group, this paper analyses five kinds of meshes used to define the mesh system behind geometric patterns and seventeen types of symmetric groups based on translation, rotation, mirror projection, and two-dimensional continuous pattern.The law of composition of Islamic geometric ornaments is analyzed by the equal-symmetry transformation of sliding mirror.
【作者单位】：石河子大学师范学院;
【基金】：国家社科基金西部项目“新疆民俗数学研究”(项目编号:13XMZ029)
【分类号】：O152

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