1. Research about dividing an angle into three equal parts Taniuchi Kazuki Tamura Yuta

2. We studied about dividing an angle into three equal parts.

3. We took an interest in many difficult math problems, especially the problem of dividing an angle into three equal parts.

4. As you know, we can divide an angle into two equal parts only with a compass and a ruler. However, it was thought that we can’t divide the angle equally in three parts with only these tools.

5. We thought it is mysterious

6. First, we studied its history.

7. Its origin hasn’t been revealed yet.

8. In the Greek age, some Greek mathematicians could divide an angle into two equal parts, but they couldn’t divide an angle into three equal parts because the problem of dividing an angle into three equal parts was too difficult to solve for them.

9. In addition, all their trials were contradictory to Platon’s rule, therefore they began to think that dividing an angle into three equal parts was impossible.

10. Platon’s rule defines the rule of dividing an angle into some equal parts.

11. According to the rule, we could use only a compass and a ruler to divide an angle equally.

12. Using only these two tools, we can do the following things. 1. drawing a straight line through two points 2. drawing a circle with a compass

13. Later, Gauss pointed out that dividing an angle into three equal parts was impossible, and a French mathematician Wantzel proved that dividing an angle into three equal parts was impossible for the first time in 1837.

14. However, we can divide ANY angle such as 45°72°90°or 180°into three equal parts. By the way, everyone, can you imagine how to divide a 90°angle into three equal parts?

15. Now I will divide the angle of 90°into three equal parts.

16. We discovered a way of dividing every angle under 90°using a piece of paper in the course of our study.

17. We proved why the way I practiced right now is correct.

18. Thank you for your attention, and I’d be happy to take your questions.