科赫曲线的产生及其影响  

The Generation and Influence of Koch Curve

作　　者：江南[1,2] 曲安京[2] 李斐[1] JIANG Nan;QU An -jing;LI Fei(College of Science,Xi'an Shiyou University,Xi'an 710065 ,China;Institute for Advanced Studies in the History of Science ,Northwest University ,Xi 'an 710127,China)

机构地区：[1]西安石油大学理学院,西安710065 [2]西北大学科学史高等研究院,西安710127

出　　处：《科学技术哲学研究》2019年第1期100-105,共6页Studies in Philosophy of Science and Technology

基　　金：国家社会科学基金重大项目(15ZBD029);国家自然科学基金资助项目(11571216)

摘　　要：在分析严格化的历史背景下,为了解决魏尔斯特拉斯函数难以几何直观表示的问题,科赫从一条线段入手,利用递归法构造了一条具有几何直观且处处不可微的连续曲线,这条曲线呈现了分形几何最重要的性质——自相似性。受此启示,谢尔宾斯基在平面上构造了具有自相似特征的谢尔宾斯基地毯,门格尔则在三维空间中构造了另一著名分形集门格尔海绵,分形几何创始人芒德勃罗用科赫曲线成功模拟了英国的海岸线形状,从而推动了分形几何的创立和发展。Under the historical background of rigorous analysis,in order to solve the problem of Weierstrass’s function which is difficult to use geometric representation,Koch constructed a self-similar continuous geometric intuitive curve which had no tangent everywhere from the beginning of a segment line. This curve has the most important property of fractal geometry which is called self-similarity. Inspired by this,Sierpinski constructed a self-similar carpet in the plane. Menger constructed a self-similar sponge in the three-dimensional space which is also a famous fractal set. Mandelbrot was the founder of fractal geometry who simulated the model of British coastline by using Koch curve,promoting the creation and development of fractal geometry.

关 键 词：科赫曲线 连续 切线 分形几何 

分 类 号：N09[自然科学总论—科学技术哲学]