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【多面體花園】

Written by helen, on 02-06-2015 02:16

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沒有可用的翻譯。

「數學上,多面體的領域值得投以特別得關注。建構出實體的模型可以讓我們領略對稱性與結構性之美。一旦我們第一次做出一組柏拉圖立體後,我們不僅得到知識性的啟發,更從中得以發想出這些模型上各種變化的新構想。」— 荷蘭籍雕塑藝術家Rinus Roelofs

 

由三角形入門,領略【多面體花園】之美:

 

 
 
我們印象中的花園是什麼樣貌呢?艾雪(M.C. Escher 1898- 1972)在「平面鑲嵌」(Regelmatige Vlakverding, 1958)一書中,生動的描述了一個【花園】:

 

(英文由Rinus提供,我轉譯為中文如下:) 

 


I walk around there all alone in that beautiful garden, which by no means is my property, and its gate is wide open to everyone.

我獨自漫步在那美麗的【花園】中,它絕不是我個人的資產,它的大門是對每個人敞開的。



I tarry in invigorating, but also oppressive solitude. And therefore I testify for years of existence of this idyllic spot, and therefore I compose this book together from images and words, without being expected that many hikers come. Because what interests me and what I experience as beauty, others deem apparently often dull and wearily.

我駐足在歡欣鼓舞,同時也沈悶孤寂的情緒當中。因此,我見證了這個宛如田園詩般景致的經年存在。也因此,我撰寫了這本圖文並茂的書。雖然,我並不期待眾多的行者,將因著這本書在這【花園】留下腳蹤。因為,我所經歷並關注與熱衷追求的美,顯然往往被其他人視為枯燥、無聊的。



在一些理論性的數學段落後,艾雪繼續描述這個【花園】:



From mathematical side is the regular tiling of the plane considered, because it forms part of the crystallography. Therefore it belongs exclusively to mathematics? I do not think so. Crystallographers have given a definition of the concept, investigated and determined which and how many systems or ways exist to evenly distribute a plane. They have thereby opened the gate giving access to an extensive domain, but they themselves did not go inside. Their kind of interest implies that they be more interested in the way in which the gate is opened than in the garden that lies beyond.

看待平面鑲嵌為數學,是因為它是構成結晶學的一部份。因此,它就專屬數學嗎?我並不這麼認為。結晶學家已探究並確定均勻分配平面的系統與方式,並且給予定義。他們由此打開了造訪一個廣泛領域的大門,但是,他們自己卻沒有進去。這意味著,他們著眼於如何打開這道門的方式,而不是門後的那座【花園】。



艾雪接著繼續描述他在【花園】中漫步的方式,詫異於眼前所發現的美麗事物:



(To keep this metaphor for a while:) long ago, while I was wandering, I came accidentally near that domain; I saw a high wall and, because I had a premonition of something mysterious, something that might be hidden behind that wall, I climbed with difficulty over. But at the levitra from canadian pharmacy update other side, I landed in a wilderness, where, with a lot of efforts, I had to find my way, until I finally found the open gate, the open mathematical gate. From there you can see well-ordered paths, going in all directions and since then I go there often and only today repeatedly. Sometimes I think I've crossed the whole domain, and then suddenly I find a new way and I taste a new delight.


(將這個譬喻保留一下:)很久以前,當我漫無目的地閒蕩著,我意外的接近了那個領域。我看到一面高牆,我強烈地感受到一種徵兆,某種玄秘的東西,在這高牆的另一邊。所以,我使勁的爬過這座牆,千辛萬苦的來到了牆的另一側,眼前卻是一片荒煙蔓草,我必須自己摸索方式生存下去。最後,我總算找著了那扇大門,一扇數學的大門!從那兒開始,我眼界所見的皆是整齊劃一的道路,通往四面八方的道路!所以,我便竭盡所能的經常造訪此地,日復一日。有時候,我認為自己已經跨越整個領域,不過,新的方式卻嘎然降臨,讓我屢屢品嘗新的喜悅。

 
 
五月,在賽爾維亞首都貝爾格萊德Rinus展示分享了這座【多面體花園】,下一座【花園】將在哪裡盛開呢?
 
 
 

Last update : 02-06-2015 05:24

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