A video on youtube

I just noticed a video "串珠與奈米世界的火花 (Sparkling Between Beading and Nano World)" on youtube which was apparently made by my school, National Taiwan Unversity.


The photos in this video were taken by Ying-Rong Chen.

Beautiful photo of Chern's C60@60 at the Columbia Secondary School

The superbuckyball, C60@C60, made by Chern is now on exhibition at the Columbia Secondary School, New York. This is for an event called MoSAIC—Mathematics of Science, Art, Industry, Culture—the festival, an offshoot of the annual Bridges Organization international conference dedicated to the connections between art and mathematics.

There is a nice photo of this C60@C60 in the Columbia Spectator.

國語日報報導 (report from the Mandarin's Daily News)

昨天到科教館參加「探索化學世界」的開幕，碰到不少記者，也是第一次跟那麼多記者講話。國語日報記者陳祥麟與陳壁銘替我跟zometool準晶模型拍了幾張照片，寫了一個有關串珠的報導：

分子結構像串珠　教授動手做模型 (2012/12/30)

I met a few local reporters in the opening ceremony of "The wonderland of chemistry" held in the National Center for Science and Education yesterday. This was the first time I talked to so many reporters. A photographer from the Mandarin Daily News (國語日報), a traditional Chinese children's newspaper published daily in Taiwan (wiki), took a picture of me with the giant Zometool model of quasicrystal hung under the ceiling in the exhibition room. The reporters of the Mandarin Daily News also wrote a report about my bead models in Chinese.

NTU newsletter: Chemist Builds Intricate Nanomolecular Models with Beads

I was told by a secretary of Science school of the NTU (National Taiwan University) early this year that they wanted to write about the beaded molecules. But I didn't know that they really wrote something in the June issue of NTU newsletter until now.

「科學的藝術、藝術的科學」 for NTU Newsletter

I wrote a few words in Chinese for the NTU Newsletter yesterday.

科學的藝術、藝術的科學
一線千珠串出繽紛多彩的奈米世界
臺灣大學化學系 金必耀

Principles for the Development of a Complete Mind:
Study the science of art.
Study the art of science.
Develop your senses - especially learn how to see.
Realize that everything connects to everything else.
Leonardo da Vinci

化學是一門研究微觀物質組成、結構、性質與其變化的科學;幾何是一門有關大小、形狀與空間關係的數學;而藝術則是人類透過情感的反應與探索所創造出的結果。我的實驗室在過去數年，無意間發現科學與藝術一個意想不到的交會，即傳統串珠工藝可連結到微觀的奈米世界的各種結構，進一步再由繽紛多彩的奈米分子世界回饋到串珠立體幾何藝術的創作。

串珠工藝有很長遠的歷史，遠古人類就已經開始使用珠子與線，製作出項鍊、手環、吊飾等各種形狀的飾物。僅需要珠子與線，透過適當的編織程序，不但可做出各種有趣的立體串珠結構，還可以用來建構正確的微觀分子與奈米結構，而且化學鍵的飽和性與方向性自然地反應在串珠分子模型中。粗略地了解微觀分子構造，可以不用進行任何量子力學的計算，不用解薛丁格方程式，不用談到原子軌域，因為建構串珠模型就好像是進行一個分子類比計算，計算的結果便是分子中的價電子密度的近似分佈。

我們的工作以芙類分子與石墨烯結構為主：包含碳六十、碳七十、與其他籠形芙類分子串珠模型；還有含有五七邊形的甜甜圈形狀的環形碳管、螺旋碳管、與三葉結碳管（圖一）；以環形碳管的內側為建構單元，還可發展出具有特殊拓樸結構的高孔洞芙類分子；更為精采的結構是無限延伸的週期最小曲面，這些結構還可細分成單度、雙度與三度週期最小曲面，三度週期最小曲面中的 P、D、G（圖二）、I-WP 等曲面是我們整個探索過程中最精美的一段歷程。除了芙類分子等三價體系，串珠也可用來建構其他類型的微觀結構，如烷類分子、金屬串分子、柏拉圖體、阿基米德體、Sierpinski 碎形結構等。

製作串珠分子模型可幫助我們更清楚地了解到分子的鍵結排列方式，如何影響分子在三維空間的結構，強化對分子結構與化學鍵的概念，更重要的是由奈米世界所啟發出來的許多串珠結構本身，就是一個精美的藝術品，不但可以怡情養性，甚至啟發一些科學想法。科學的藝術作品除了能讓人讚佩其優美之外，隱含於其中的數學與科學原理，更能讓人進一步沈思自然的奧妙。

圖一: 三葉結碳管

圖二: 螺旋型（Gyroid）三度週期最小曲面

Structural rules of high-genus fullerenes

Some people asked me about the pattern for making a high-genus fullerene. It is quite difficult to explain. Previously, I have posted two series pictures for creating two types of high-genus fullerenes: one consisting of octagon necks and the other for pentagon necks. They should be clear enough for anyone who try to create one.

If you want to create high-genus fullerenes in addition to these two HG-fullerenes. You have to follow more general structural rules. C. Chuang has worked out very general structural rules for constructing high-genus fullerenes belonging to tetrahedral, octahedral and icosahedral groups last year. The details have been described in this paper:

1. "Systematics of High-Genus Fullerenes." J. Chem. Inf. Model. 2009, 49, 1664-1668. DOI: 10.1021/ci9001124, ACS News & Research, July 2009.
pdf

Interestingly, this paper on the classification of High-Genus fullerenes has appeared in the "News & Research" session of ACS homepage http://portal.acs.org in July 2009.

Wonder How To

WonderHowTo site has said something about us: Mathematical Beading: Accessories to Thought.

Carnival of Mathematics #67

My site has been mentioned in Carnival of Mathematics #67.

【科學工藝】化學家用珠珠串出富勒烯家族 Scientific Crafting: Chemists Construct Fullerenes with Beads

The blog of Case (Case Press) has written something about us in Chinese.

Here are a few photos taken by the photographer (張譽鐘) of Case (Center for the Advancement of Science Education), National Taiwan University.







(High-genus fullerene with octagonal necks, No:3)

Math Monday: Mathematical Beading

The fullerene structures that we have created have been featured in Math Monday for the Make Magazine blog.

Math Monday, written by George Hart, is a weekly column in a partnership between the Museum of Mathematics and Make Magazine. This column discusses fun, experiential, puzzling topics in mathematics.

Beaded Fullerenes: 3D Molecular Structures

The blog "The Beading Gem's Journal " has featured the 3D molecular structures that we have constructed. :-)

Paper appeared as an item in ACS homepage

My paper with Chuang on the classification of High-Genus fullerenes has appeared in ACS homepage http://portal.acs.org in July as an item in News & Research.