A pleasure to greet two friends from afar

Takaaki Sonoda and Kazunori Horibe visited me for the last few days. I arranged a few workshops for them in two local high schools, Taipei First Girls High School and Chian-Kuo High School, and a meeting on the mathematical art and games. A few photos from these activities:

Taipei First Girls High School

Chien-Kuo High School

Little Mama Bear (bead store)

Math department, Academia Sinica

Inside the cubic Kaleidoscopes

I made a Kaleidocycle and a stella octangula for them as gifts:

Unfortunately, Takaaki didn't know that they are fragile and broke the stella octangula the first day. So I made one more Kaleidocycle for him.

The opening of the Analects by Confucius and thus the first phrase of Chapter I after which the Chinese title of this book is named 學而.

學而時習之、不亦說乎。有朋自遠方來、不亦樂乎。人不知而不慍、不亦君子乎。

Isn't it a pleasure to study and practice what you have learned? Isn't it also great when friends visit from distant places? If one remains not annoyed when he is not understood by people around him, isn't he a sage?

Cube kaleidoscope (Wonder Mirror Box, or CUMOS cubic cosmos scope)

N asked me about the cube kaleidoscope Chern posted before. If you are interested in getting instructions and materials for making your own cube kaleidoscope, you should contact Prof. Takaaki Sonoda (園田 高明) of Kyushu University (九州大學). (reports about him in Czechish??? and in Japanese).

Here I just want to show the other two cube kaleidoscopes, kaleidostereochemistry and kaleidogarden, I made when Prof. Sonoda visited Taiwan about one year ago.

It is really fun to make your own kaleidoscope. Basically, one needs to have six mirrors to make a cube kaleidoscope. Once you have the necessary materials, you need to make patterns on two or three mirrors by scratching part of mirror away by using suitable stick. For details, please contact Prof. Sonoda.

In addition to the two kaleidoscopes I made by myself, I also got another professionally made cube kaleidoscope from Prof. Sonoda as a gift.

You can also find extra information at this site (CUMOS cubic cosmos scope). Here is one I found at that site:

More images is in this gallery.

The Cubic Kaleidoscope I Made Today

Looking along the (1,1,1) direction:






Outside:


I gave it the name of "PlatoKaleido". Because this is in fact the three Platonic tilings, square planar(purple+red), equilateral triangular(orange+yellow) and honeycomb(green+blue) lattices, inter-penetrating one another orthogonally. The coloring is in accordance to the order of the spectrum of sunlight, if you notice. It is a great fun making this kind of kaleidoscopes, thanks to Prof. Takaaki from Kyushu University who kindly taught us earlier today.

My supervisor Bih-Yaw mentioned about the possibility of making this kind of kaleidoscope with other geometric shapes like triangular or pentagonal prisms. And Prof. Takaaki replied that they'd been trying everything possible already. However, I am thinking about using non-planar mirrors instead, e.g. concave or convex, making the "metric" of the wondering world therein non-Euclidean, maybe an interesting task. This is also related to some photos taken by Bih-Yaw at this year's Bridge conference. The artist made clever use of the curvature of the mirror, so the image of an seemingly unreasonable object on the mirror becomes a normal one (of course in this case the images are in fact the unreasonable structures that the artist tried to convey).