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

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「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




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】:




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.


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.



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.



(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 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 repeatedly. Sometimes I think I've crossed the whole domain, and then suddenly I find a new way and I taste a new delight.



Last update : 02-06-2015 05:24

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