几何形式、透视法与自然的认知观

South Architecture - - 第一页 - 1 2 4 闫珮珮 李雪 田 田朝阳 Yan Peipei Li Xue Tian Peng Tian Chaoyang 3

Geometrical Forms, Laws of Perspective and Views of Nature

摘要 基于欧氏几何与分形几何的不同透视观法的分析可以看出,几何形式与透视观法存在必然联系:西方古典园林因欧氏几何形构图制造了静止的空间而采用定点透视的观法;中国古典园林因分形几何构图制造了动态的空间而采用动点透视的观法。欧氏几何与定点透视的观法浑然一体,分形几何与动点透视的观法浑然一体,发展出两套截然不同的美学体系。认知论决定了方法论,中西方园林几何形式与观法的不同根源在于自然观的不同,西方是控制自然从而简化自然,中国是尊重自然从而模拟自然。

关键词 欧氏几何;分形几何;透视法;自然观abstract Based on the analysis of the different perspective views between Euclidean geometry and fractal geometry, a direct correlation is drawn between geometry and the laws of perspective :Western classical gardens creates static spaces based on Euclidean geometric composition by using fixed-point perspectives, while Chinese classical gardens creates dynamic spaces based on fractal geometrical composition by using dynamic perspectives. Euclidean Geometry comes with fixed-point perspective, while fractal geometry comes with dynamic perspective, each developing its distinctive aesthetic system. Epistemology determines methodology. The root of the different geometries and perspectives between Chinese and western gardens is due to the different views towards nature. The western way is to simplify nature through controlling it, while the Chinese way is to imitate nature through respecting it.

KeY Words Euclidean geometry; fractal geometry; laws of perspective; view of nature

中图分类号 TU986文献标识码 A

DOI 10.3969/j.issn.1000-0232.2017.02.112 文章编号1000-0232(2017)02-0112-05

1&2 3 4

作者简介 河南农业大学林学院,硕士研究生; 苏州园林设计院,助理工程师; 河南农业大学林学院,教授,通讯作者,电子邮箱 :tcytcytcytcytcy@163.com

古代希腊数学家欧几里得创始了几何学,简称欧氏几何。1482年欧几里得几何学从阿拉伯语译成拉丁语,带给设计者对黄金分割的几何学理解。圆、方、比例和几何图案被使用在设计中,透视用来统一绘画和建造项目,用来将建筑和园林连为整体 [1]。1975 年,美籍法国数学家曼德勃罗特首次提出“分形”(Fractal) 一词,并于 1977年出版第一本著作“分形:形态,偶然性和维数” (Fractal:From,Chance and Dimension),标志着分形理论的正式诞生[2]。有学者证实了中国园林运用了分形几何 [3]。

1数学中的几何与透视

欧氏几何与分形几何是人对世界认知的产物,透视是观察世界的观法。二者之间的关系如何呢?图1中方、圆、三角形的欧氏几何形是从沃- 勒 -维贡特庄园中抽取的,分形是从退思园中抽取的。从a点用定点透视的角度看方形(图2),基于完形理论 [4],我们能感知到全貌。

图 1几何形的感知

图 2欧氏几何形的动点感知

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