The OCU Graduate School of Science research group of Professor Akio Kawauchi (Director of Osaka City University Advanced Mathematical Institute (OCAMI)), Ayaka Shimizu (researcher at OCAMI) and Kengo Kishimoto (former researcher at OCAMI) has succeeded in creating a game applying knot theory, tentatively titled "Region Select".

It is very rare that the purely mathematical knot theory is practically applied. However, as you do not need any mathematical skills to play the game, it is suitable for young and old. It has the potential to be used in primary school education and in rehabilitation training of cognitive functions. Patent has been filed for the game mechanics and program. You can play the game on OCAMI's website:
http://www.sci.osaka-cu.ac.jp/math/OCAMI/news/gamehp/etop/gametop.html

Background of the research

Usually, a knot is simply a tied string, but scientifically speaking it is a string that closes a 3-dimensional loop. Knot theory mathematically researches what kind of knots there are and whether two knots are identical. In recent years it drew interest through joint research in physics, science and biology. Since the mathematical department of our university was chosen for the 21st century Center of Excellence (COE) program, it has produced many interesting research results in knot theory?

Game outline

In the electronic knot theory game, you see a knot projection, namely a picture with one line of which the ends meet and which crosses itself at least once. At each point where the line transversely crosses itself is a light that is either on or off. When you click on an enclosed field the crossing points that border that field turn on or off. The goal is to turn on all lights by clicking on fields in a correct order.

How to play

Although there are other well-known games that apply mathematics, such as the Rubik's Cube and Sudoku, this knot theory game does not use any letters or numbers, and can therefore be enjoyed by people of all ages, with or without mathematical skills.

Future development

Since knot theory proves that this game can always be finished in a finite time of clickings for any knot projection, players can freely draw their own shapes to create new tasks. As it is possible to set the degree of difficulty, it can also be used in primary education and for training cognitive functions to recognize shapes during rehabilitation. Finally, the game has potential to be applied in new ways of lighting lamps in lighting equipment and other industrial fields.