{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"a6cc7da8-99f2-4538-8a66-26787f7481a3","title":"资本主义与精神分裂(卷2)：千高原(修订译本)","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787208178977","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"a6cc7da8-99f2-4538-8a66-26787f7481a3","id":"a6cc7da8-99f2-4538-8a66-26787f7481a3","uuid":"a6cc7da8-99f2-4538-8a66-26787f7481a3","title":"资本主义与精神分裂(卷2)：千高原(修订译本)","normalized_title":"资本主义与精神分裂卷2千高原修订译本","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787208178977","isbns":["9787208178977"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":515,"navigation_url":"https://workshop.closeclaw.top/ai/book/a6cc7da8-99f2-4538-8a66-26787f7481a3","title_url":"https://workshop.closeclaw.top/ai/title/%E8%B5%84%E6%9C%AC%E4%B8%BB%E4%B9%89%E4%B8%8E%E7%B2%BE%E7%A5%9E%E5%88%86%E8%A3%82(%E5%8D%B72)%EF%BC%9A%E5%8D%83%E9%AB%98%E5%8E%9F(%E4%BF%AE%E8%AE%A2%E8%AF%91%E6%9C%AC)","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/a6cc7da8-99f2-4538-8a66-26787f7481a3/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/a6cc7da8-99f2-4538-8a66-26787f7481a3/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/a6cc7da8-99f2-4538-8a66-26787f7481a3","page_url":"https://workshop.closeclaw.top/api/ai/books/a6cc7da8-99f2-4538-8a66-26787f7481a3/page","search_url":"https://workshop.closeclaw.top/api/ai/books/a6cc7da8-99f2-4538-8a66-26787f7481a3/search"},"page":{"printed_page":457,"pdf_page":475,"physical_index":475,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"18db2703730ef60cad618c8d95bca430df156cea1ae19bb147581ee5f23a1b0e"},"chapter":"Capitalisme et Schizophré Mille Plat Dilles Del ix Gu","content":"冯·科赫曲线：大于一条线，小于一个面！线段AE（1）的中点被去除，置换为三角形BCD（2)。而在图（3)之中，此种操作被分别重复于线段AB，AC，CD和DE之上。如此就形成一个多角状的线（4)，它的所有线段都是相等的。在图形（4）的各条线段之上，我们再度重复之前在（2）和（3）之中已经进行过的操作；如此以至于无穷。最后，我们就得到了一个由无限多的角状点所构成的“曲线”，它在任何一个点上都不允许有切线。这条曲线的长度是无限的，它的维度高于1：它再现了一个1.261859 维的空间(准确说是 log 4/log 3)。\n\n谢尔宾斯基(Sierpinsky）海绵，大于一个面，小于一个体！这个立方体据以被穿孔的法则很容易进行直观上的理解。每个正方形洞的周围都有八个小正方形洞，每个小正方形洞的面积都是它自身面积的三分之一。而每个小正方形洞周围又有八个更小的正方形洞，其中每一个的面积是它自身面积的三分之一。如此以至于无穷。图示无法再现这个洞孔趋于无限微小的过程，它至多只能达到第四次操作的层次，但很明显，这个立方体最后会被无限挖空，它的总体积将趋于零，而它的被挖空部分的总表面积则趋于无限增长。这个“空间”的维度是2.7268。因此，它介于面（二维）和体（三维）之间。“谢尔宾斯基地毯”则只是这个立方体的一个面，在其中，被挖空部分是正方形，而这个“面”的维数则是1.2618。(转引 自 Leonard Blumenthal and Karl Menger, Studies in Geometry, Freeman and Company, 1970)\n\n关于伯努瓦·曼德勃罗的“分形客体”\n\n14. 1440年：平滑与纹理化\n\n457","previous_page":456,"next_page":458}