Cooperation of KeTCindy and Computer Algebra System

Abstract

In Japan, some wooden plaques presenting geometrical puzzles (SANGAKU) show problems of drawing smaller circles within a larger circle in contact with it or a circle in contact with a quadratic curve, such as an oval. Problems of these kinds can be interesting teaching materials. Dynamic geometry software such Cinderella or GeoGebra is useful to solve these problems. One can use high-quality TeX graphics with KeTCindy (Cinderella plug-in) to draw these figures. One can also draw figures by solving simultaneous equations using a computer algebra system such as Maxima or Risa/Asir. Although simultaneous equations can be solved in Maxima, the solution takes time. Alternatively, it does not work when too many variables are included. In such cases, one can convert it to a system of equations that are easier to solve using a Grobner base in Risa/Asir. Then a user can solve them by giving the result to Maxima. A user can accomplish this on Cinderella through KeTCindy, and can draw circles using the result. This method can also be applied to other difficult circumstances. This paper presents some examples.