### Sangaku ( under construction )

I found a picture of this sangaku in internet.
On October 4, 1999, I purchased a real one at Isaniwa Shrine in Ehime
Prefecture.

This "sangaku" shows off that an 11-year-old boy solved a
geometry problem. Its approximate meaning is as follows:

Suppose the fan in the figure is 1/3 of the complete circle.
As is indicated in the figure,
one east circle, two west circles, two south circles
and
two north circles
are constructed. Suppose the the diameter of the south circle
is given. What, then, is the diameter of the north circle?
Answer
Multiply the diameter of south circle by ( sqrt(3072) + 62 )/193.
You have the diameter of the north circle.
Meiji 6th ( 1873 ), December
Kinjiro Takasaka 11 years old, a student of Master Shoryu Yamazaki.

My comment: There is no indication to which circles are east,
which are west, ... Judging from the answer, the red one is
north and the white one is south. A picture of the fan which I draw is
here.

An answer was given to me by Prof. A. Craik
of St. Andrews University.

If you have not read the following internet articles, then
it might be interesting to you.

### Links