对称与图形创意──基于图形组织结构的数学原理与应用(英文)

Symmetry and developing ideas:Construction-based approach to geometry of two-dimensional pattern designs

艺术家已经意识到“对称”在图形设计以及对形成有规律的从复的图形组织结构的辅助作用。所谓对称,是指设计中的部分内容(母题)在某种数学几何原理的驱动下,有规律地向整个二维平面伸展从而形成完整的设计.在二维平面,总共有四种几何变换(对称操作规程)方式,数学家称这种变换isom etrics(来自希腊词isos=equal(同等)m atron=m easure(测度)。分析从复对称的图形,研究如何遵循数学“法则”等活动,动机不在于数学本身。明显地,“对称”具有双重词义,艺术的与数学的含义是不可分离的。

Many of the graphic designs found in commercial and decorative art possess symmetry： A part of the design （ a motif） is repeated regularly to create the whole design. There are just four different ways in which a motif can be related to a congruent copy of itself if this relationship is described in terms of geometric transformations which preserve shape. To analyze a repeating design to see what makes it＂work＂, and to create original designs using the power of the mathematical ＂laws＂ which govern these designs, is a strong non - mathematical motive for studying these theories. Obviously , the word ＂symmetry ＂ has true dual meaning; Both its artistic and mathematical connotations are seen as inseparable.