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
             two north circles

are constructed.  Suppose the the diameter of the south circle
is given.  What, then, is the diameter of the north circle?


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.