1. Japanese Wazan Mathematician
Seki Takakazu
Japanese Wazan Mathematician
I’d like to introduce Takazu Seki and his calculations of a value of Pi.

2. Japan “Closed off”
(1616 – 1853)
In 1616, Japan closed itself off from the outside world and it lasted about 300 years. Thus, in that era, Japanese mathematicians couldn’t gain or exchange knowledge with foreign countries. This is one of the reason why Japanese mathematics grew in a unique way and was called “Wazan”.

3. Seki was a contemporary with Isaac Newton
Seki was a contemporary with Isaac Newton. But they never knew each other.
Now this traditional Japanese mathematics is still studied by researchers separately from regular mathematics.
Seki was one of the greatest Wazan mathematicians of the era. He was born in a Samurai family in 1642.
He was a contemporary with Isaac Newton, but they never knew each other.
Isaac Newton（ )
English mathematician
Seki　Takakazu（ )
Japanese mathematician

4. Value of pi
He started studying mathematics on his own and that talent was discovered by the family when he was nine years old.
One of his famous studies is calculation of a value of Pi which is correct to the 11th decimal place.
He inscribed a polygon with sides in a circle to calculated Pi radius square.

5. Polygons approximate to circle
When radius = 1, the area of the circle is found by Pi.
As the number of the sides increases, a polygon approximates to the circle. So he calculated an area of polygon with the largest number of the sides he could calculate at that time.

6. Polygons approximate to circle
Let’s think about a square, which is inscribed in a circle. The square has four sides and those sides are away from the circle’s perimeter even all the corners of the square touch it. Also, the shape of a square doesn’t look similar to circle.
How about octagon?
It has eight sides and the shape of a octagon looks similar to the circle than square.
Then, divide to octagon diagonally to make eight triangles and re-arrange it so as to look like a rectangle.
The long side consists of the sides of the octagon. This says the total length of the long sides are approximately equal to the circle’s perimeter.

7. The more sides a polygon has, the better approximation of pi it provides.
Polygons
Lengths of one side
Total length of the perimeter 8 16 32 64
128
256
1024
2048
4096
8192
16384
32768
The more the number of the sides is increased, the value gets closer to the circle’s perimeter. This is his methods.
He was known as an expert, but his profession was an official auditor of the government, for it is one of the traditions of Samurai families to be a public servant. He studied mathematics in between his job and even had a lot of students. It is not a privilege only for professional mathematicians to pursue one’s interest. It is important for us to think about the questions with enthusiasm.