2014 NTU Summer Chemcamp (臺大暑期化學營)

These few days, there is a chemistry camp at the Chemistry Department of National Taiwan University (NTU). I was asked to give a workshop on the last day (Jul. 10, 2014) of this activity for these high-school kids coming from around the whole Taiwan and the Penhu islands (or the Pescadores Islands). The camp started yesterday afternoon, I had an opportunity to introduce them briefly about my beadworks in front of two display cases. Here are two photos from the event:

The first few pages of the handout for this chemcamp.

Workshop in Seoul

Mr. Horibe and I will give a workshop for the Bridges conference this coming August. Basically, we will follow the format we had in our joint workshop given in Taiwan this March. Horibe-San will first give a half-hour talk on the Sangaku in general and a special Sangaku problem in particular. And he will further describe the math about this Sangaku problem, particularly its connection to the continued fraction and then proceed to the construction of a physical model of this Sangaku problem before all participants make their own models that consist of 30 small wooden balls and a central large Ping-Pong ball.

Here are two photos of Mr. Horibe from workshop held in the math department of Academia Sinica (in the NTU main campus, Taipei) on Mar. 15.

The workshop paper, From Sangaku Problems to Mathematical Beading: A Hands-on Workshop for Designing Molecular Sculptures with Beads, can be found here (pdf file).

The Brazuca and octahedral fullerenes

Yuan-Jia and I submitted a manuscipt entitled, From the "Brazuca" ball to Octahedral Fullerenes: Their Construction and Classification, to the physics preprint archive, arXiv, recently. Basically, we observed that the symmetry of the Brazuca ball used in the FIFA World Cup held now in Brazil is exactly that of an octahedral fullerene, which Yuan-Jia has been thinking about for more than a year. Therefore, we modified the original manuscript a little bit to point out this peculiar connection. Hopefully, researchers can know that not only the original the Adidas Telstar, a truncated icosahedron, has a microscopic analog, namely the famous C₆₀, the current Brazuca ball could also have microscopic correspondence, in principle.

The Adidas Telstar vs a C₆₀ molecule

The Adidas Brazuca vs an octahedral fullerene

Here I give a list of symmetry groups for all official match footballs (soccer balls) adopted by the FIFA since 1970:

Year	Country	Name of the official match ball	Point group
1970	Mexico	The Adidas Telstar	Ih
1974	West Germany	The Adidas Telstar Durlast	Ih
1978	Argentina	The Adidas Tango Durlast	Ih
1982	Spain	The Adidas Tango Espana	Ih
1986	Mexico	The Adidas Azteca	Ih
1990	Italy	The Adidas Etrvsco	Ih
1994	USA	The Adidas Questra	Ih
1998	France	The Adidas Tricolore	Ih
2002	Korea Japan	The Adidas Fevernova	Ih with T pattern
2006	Germany	The Adidas Teamgeist	Th
2010	South Africa	The Adidas Jabulani	Td
2014	Brazil	The Adidas Brazuca	O

It is interesting to note that it took FIFA 28 years to move away from the icosahedral symmetry to the tetrahedral symmetry, and then another 12 years to come to the last of three Platonic symmetry groups, namely the octahedral group. Another peculiar difference between the Brazuca ball and the previous soccer balls is the lack of inversion and mirror symmetries in the Brazuca ball, meaning that the Brazuca ball is chiral. This should lead to nonvanishing coupling between translational and rotational (spinning) motions, I suspect.

Tetrahelices - two bead models of Boerdijk–Coxeter helix

There is a helical tower based on the Boerdijk–Coxeter helix in Mito-shi, Ibaraki-ken, Japan:

Art Tower MIT

So, during my visit to Nagoya this May, I made several tetrahelices as souvenirs for my friends there. Since I brought many tubular beads with different colors to choose from, so I decided to use different color for three helical edges in each tetrahelix. In total, there should be four possible arrangements or two enantiomer pairs. But I only made two of them shown in the following picture. After I made these two tetrahelices, so many people also like to have this model, so I made two more tetrahelices before I left Japan.

A few photos from workshop in the Nagoya City University

During my visit to Japan this May, Prof. Sonoda and Horibe kindly arranged a special workshop in the Nagoya City University on May 10, 2014. Here are a few photos from the workshop which connecting the Sangaku problems and mathematica beading.

In addition to this workshop, Horibe and I will also give a similar workshop in the Bridges meeting (Seoul) this year.

High-Genus Fullerene