Workshop at BCCE, Grand Valley State Univ.

I will give one more workshop in the 2014 Biennial Conference on Chemical Education which is hosted by the Grand Valley State Univ, Michigan next week. My workshop is arranged in the afternoon (2:00-5:00PM) of Aug. 4.

It is free. Hopefully, I brought enough beads with me for every participant.

"Mathematicians Solve The Topological Mystery Behind The “Brazuca” World Cup Football Just in time for the World Cup final"

I just noticed that there is a page from Medium - Everyone’s stories and ideas,
Mathematicians Solve The Topological Mystery Behind The “Brazuca” World Cup Football Just in time for the World Cup final,
which reported the manuscript, From the "Brazuca" ball to Octahedral Fullerenes: Their Construction and Classification, Yuan-Chia Fan and I submitted to the arXiv at the end of last month.

In fact, Yuan-Jia has been working on the general structural rules for this peculiar family of generalized fullerenes with octahedral symmetry for a period of time. When the FIFA World Cup started in the mid June, I noticed quite accidentally that the official soccer ball, the “Brazuca”, for the FIFA World Cup held in Brazil this year has exactly the same octahedral symmetry. Then, we rewrote the draft a little bit and changed the title to its current form. However, the manuscript was first rejected by the Journal of Chemical Information and Modelling because the paper is not of general interest to the readers of the journal. And then it was rejected again by the Journal Physical Chemistry A because the editor thought this paper falls outside the bounds of the journal.

Instead of finding another journal, I decided to put it in the print archive, arXiv, at the end of June. So people might find it interesting during the World Cup season.

The evolution of the official Adidas Soccer Balls since 1970.

In addition to the page on Medium - Everyone’s stories and ideas, I also noticed three more pages which refer to the Yuan-Jia's work on the octahedral fullerenes and their connection to the Brazuca:

• Physics World: Molecular footballs, knotty headphones and a naming contest for exoplanets.
• Brazuca, la scienza a servizio del calcio (Italian)
• Il Brazuca e i ‘misteri topologici’ dietro i palloni dei mondiali (Italian)

Workshop for the NTU CampCamp

The first few slides and a few photos from the workshop I had for the NTU ChemCamp this afternoon in the Chemistry Building of National Taiwan University:

First slides for my talk in Center for Synchrotron Radiation and workshop for the Chemcamp

I have two opportunities to talk about the mathematical beading this month. The first one was given to people working at the Center of Synchrotron Radiation on Jul. 1. The first slide of the talk is given here:

Tomorrow I will give a 40-min talk before the hands-on workshop for about 30 high-school students who participate the Chemcamp these few days. The first slide of the talk is given as follows.

Another two workshops in this summer

In addition to the workshop in Seoul, Korea for the Bridges conference, I will give two more workshops in this summer: the first one is for the Chemistry Camp in the chemistry building (積學館) of the National Taiwan University this Thursday (1:30PM-5:00PM, Jul. 10, 2014) and another one for the 2014 Biennial Conference on Chemical Education (BCCE, Aug. 3-7, 2014) which will be held in the Grand Valley State University (Michigan, USA). My workshop in BCCE is on Aug. 4, 2014.

The weight of mathematics

Is there a weight for a mathematical problem? The answer is Yes, if you talk about the Sangaku problem from the Edo period of Japan. Under the kind arrangement of Prof. Sonoda and Mr. Horibe during my visit to Nagoya this May (May 11, 2014), I was fortunate enough to see a few wooden Sangaku tablets, replica and original one, and really saw that mathematical problems can be really heavy. The next day after Horibe-San gave a workshop, Dr. Fukugawa Hidetoshi and I gave the other two talks in the Nagoya City University, we visited two temples in the Nagoya area.

Dr. Fukagawa is the premier authority on the Sangaku tablets in Japan. But he had a serious cold in that weekend, but still insisted to go with us to visit these places. In addition to him and me, we were also jointed with Mr. Horibe, Prof. Sonoda, one local high school math teacher to see these Sangaku wooden tablets.

The first temple we went is the Atsuta Shrine(Atsuta Jingu/熱田神宮). Right after we arrived, we were guided to a special room in the second floor by people from the Shrine, where the replica of two Sangaku tablets (dated 1841 and 1844, respectively) are carefully stored and not on display usually. Because we were special guests of Dr. Fukagawa, so we were lucky enough to have the privilege to examine these two beautifully-made replica.

After we had a brief lunch at Atsuta Shrine, Mr. Horibe brought us to a beautiful temple, Yourinzi temple (明星輪寺), in a nearby mountain area, Mount Ikeda (Ikeda-yama, 金生山) of Ogaki city, Gifu prefecture (岐阜縣大垣市). In this Buddhist temple, there is a well preserved Sangaku tablet made in 1865. Most importantly, many mathematicians and physicists, including Freeman Dyson, have been invited by Dr. Fukagawa to visit this temple to see the Sangaku tablet before.

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.