Hongtaek Hwang and Gyungsoo Woo

Professor and Director
Dept. of Applied Mathematics & Agency of Hands-on Science Class, Kumoh Institute of Technology / Changwon University
Gumi, South Korea / Changwon, South Korea

We enjoy creative activities on the boundary between Mathematics and Art. Sometimes we create artwork by using geometric tube design.

It is well known that the truncated icosahedron(TI) originated from the ancient Greek's great philosopher Plato's cosmic imagination based on mathematics. We define the regular pentagonal shape(RPS) by the rotational invariant finite figure in the period of 2π/5 radian. For a given RPS, it is possible for us to image a creative spherical pattern derived from the TI by applying the TI formation scheme. Eventually, through a series of geometric tube design experiments, we can establish a geometric reality of the creative spherical image. We call this reality the Archimedean star with respect to the RPS.

Stars over the A'lhambra Palace
Stars over the A'lhambra Palace
Geometric Tube Design

This is my geometric tube designed representation of an ancient Islamic design that originated from certain arts of seven circles. I found the ancient Islamic design in the book "Islamic Design" I bought at the museum of the A'lhambra palace. So I named it " Stars over the A'lhambra Palace" in memory of my visit to the beautiful A'lhambra palace in the spring of 2008.

Acknowledgement : This is a research result which had been established under the professor research year policy of Kumoh national institute of technology.

Platonic Water of H-Fractal 5.3
Platonic Water of H-Fractal 5.3
Geometric Tube Design

Icosahedron as one of Platon’s four ideal geometric components which form universe also is a regular polyhedron to symbolize water. The composition "Platonic water" must be the one that originates from Plato's cosmic imagination based on mathematics. In fact, it is a minimal fractal combination of certain skewed Archimedean stars and also an abstract creation derived from the design of Fullerene and Telstar.

This composition was supported by Research Fund, Kumoh National Institute of Technology