There is only one pair in the world, a triangle with special relationship. Two theorems about mathematical geometry dealing with figures were proved by two graduate students of Keio University. The theorem itself is content that even primary school students can understand. Two people are talking "I want you to enjoy the depth and fun of mathematics."

What I worked on the proof was geometric problem, "Is there a pair in which both the length and the area of ​​the circumference are equal in the right triangle and the isosceles triangle pair whose side lengths are all integers?" something like. Graduate student Yoshinosuke Hirakawa (28) and Hideki Matsumura (26), who are studying mathematics at Keio University Graduate School of Science and Engineering, began challenging last December.

First of all, they converted the geometric problem that many triangles come out into algebraic equations dealing with expressions, and replaced them with the question of how many solutions exist. Then, using the modern mathematical method "number theory geometry", we found that there is one solution.

From this result, the circumference length and area ...