Overview of our research performed by high school students.

In Kwansei Gakuin High School more than 40 students have done mathematical research using computers, and they have discovered many new theorems. They have published their results in many accredited journals and popular online magazines, and many mathematicians and computer scientists found these results very interesting.

There are very few high schools where students are constantly discovering new facts about mathematics, and for many people our research results may be incredible.

We would like to show that with the power of computers and good software high school students can be very creative.

Let's illustrate the method we used in our research.

First we and Dr.Miyadera, our teacher, look for good problems. We read mathematics books and magazines.

When we find interesting problems, we try to alter them. Sometimes we try to generalize them, and other times we change the rule of the problem. Then we get new problems.

Once we get proper problems, we use computers to analyze them.

We generate a lot of data using computers, and try to find interesting patterns in the data.

We are a lot better than Dr.Miyadera in finding patterns!

Once we discover an interesting pattern, we try to prove the pattern mathematically.

Sometimes Dr.Miyadera helps us make proofs.

Fortunately in the research we present here Dr. Miyadera did not have to help us because we only had to use mathematical induction to prove our theorems.

We hope that some students in Canada find our research interesting and contact us, so they can join our research!

We are still working on a lot of unsolved problems that are interesting and understandable to high school students.