# The missing radius in a Sangaku geometry: an old Japanese problem

Posted 10 months ago
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Posted 10 months ago
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Posted 10 months ago
 Yang-san,Thank you for all your interesting posts. I always enjoy them. The Mathematics Certification Institute of Japan celebrates Jan 23rd every year as "the day to spread the Sangaku culture." https://www.sangaku123.jp/en/
Posted 10 months ago
 Mr Okazaki, Thanks for the compliment and the link. I am working on using WL to demonstrate a large number of geometry problems and properties from this fantastic book https://www.amazon.com/Sacred-Mathematics-Japanese-Temple-Geometry/dp/069112745X. It is a wonderful journey to work with ancient sangaku problems plus modern technology.
Posted 10 months ago
 Interesting work. I have a question. How do I use this to find, either exactly or approximately, the value of the radius for the original problem (that is, with the equilateral triangle).
Posted 10 months ago
 You can change a to {1,Sqrt[3]} to form a equilateral triangle and run the attached notebook. The radius is about 0.318. Attachments:
Posted 10 months ago
 Thanks Shenghui. I had actually tried that change but for some reason the code was not working for me. Possibly I missed an initialization snippet. Anyway, it's a nice problem and solution method.
Posted 10 months ago
 From the video linked in the head post the symbolic value of the radius for an equilateral triangle is $\sqrt{3}-\sqrt{2}$ .
Posted 10 months ago
 WL indeed handles the symbolic case for equilateral triangle very well.