The authors of the paper are Hiroshi Matsui and Toshiyuki Yamauchi who are 12 grade students. Their dream is to be scientists, and H.Matsui loves chemistry and T.Yamauchi loves physics, and both of them love computer languages such as Mathematica, Java and C++ . They discovered the theorems in this paper when they were studying mathematics using Mathematica.

Faculty Sponsor: Ryohei Miyadera, Kwansei Gakuin High School, Japan