From: kishik@parkcity.ne.jp   
      
   Q.E.D. vol.38   
      
   by KATOU Motohiro   
   published by Koudansha   
   ISBN978-4-06-371270-4   
   419 yen (sans tax)   
      
   Caution: sorry, this post is LONG.   
      
   Q.E.D. is not the cryptic text editor of TOPS-10. It stands   
   for Quod Erat Demonstrandum that is used at the completion   
   of mathematical demonstration. The title is so named because   
   the protagonist Sou says "demonstration accomplished" at   
   the end of his solving a case, typically a murder case.   
   He graduated from MIT at age 15, returned to Japan and   
   entered a highschool. His class mate Kana takes a role of   
   trickster and involves him in cases.   
      
   Normally I don't buy the series because of bland artwork   
   and flat storytelling. Volume 38 has an episode of wasan   
   [old Japan's mathematics] that caught my attention.   
      
   [ episode: "Seventeen" ]   
      
   Katasumi-jinja has a small old shrine in shape of a regular   
   polygon of seventeen edges. Its inside is painted in black,   
   the floor has two lines crossed at the center where is a   
   small circle representing a zero. On the wall, many sangaku   
   [mathematics plate] are also hanged. One of the sangaku was   
   signed as "Aisa, 13 years old" and has a picture that looks   
   like a pearl necklace. Each one of twenty circles is contacted   
   to two adjacent ones and has a white portion and a black   
   portion divided by perpendicular lines starting from the   
   center of it and ending to the contact points. All black   
   portions are faced inside of the closed ring. Sou thinks   
   that it's a mathematical question to ask for the difference   
   between total area of white portion and of black. Sou solves   
   the problem and thinks further about the mystery hidden in   
   the shrine.   
      
   In Edo about 300 years ago, a famous wasan authority TAKEBE   
   Katahiro was introduced to a young girl Aisa. Takebe gave   
   her a problem to ask for the length of diameter of a circle   
   inscribed to a triangle of 10x10x12. In front of him, she   
   solved the problem with ease. So, he gave her another   
   problem. Next day, she visited him and solved the problem   
   that was the same one on the sangaku Sou solves three   
   centuries later.   
      
   Aisa explored mathematics further and found that some equations   
   had two different answers one of which didn't look legitimate.   
   Wasan didn't have concept of imaginary numbers, but she believed   
   in the answers and reached to an idea of the complex plane. She   
   tried to draw graphs of the answers of the equation X*X = 1   
   on the plane and got beautiful regular polygons. But she wasn't   
   Gauss, and couldn't make her idea a theory. So in hope of   
   someone solve the problem in a future, Aisa and Takebe built   
   the shrine as an unsolved problem.   
      
   Sou thinks that the shape of seventeen edges might suggest that   
   Aisa reached an idea of the theory during her exploration of   
   a 17 degree polynomial that also led Gauss to the theory.   
      
   [ Wasan (old Japan's mathematics) ]   
      
   In 1627, YOSHIDA Mitsuyoshi published "Jinkouki" that is a text   
   book of mathematics based on a Chinese book. In the end of the   
   book, he gave readers unsolved problems as a challenge. The   
   book got a great popularity and readers kept solving problems   
   and providing new problems. People who were interested in wasan   
   offered sangaku to shrines and temples to thank deities for the   
   solution and invention of a problem. As the result, wasan was   
   advanced significantly. The Japanese custom of sangaku was unique   
   in the history of the world.   
      
   The Japanese still refers to nezumizan [mice's calculation],   
   a topic in "Jinkouki", as a synonym of rapidly growing number.   
   e.g. "$B%$%s%?!<%M%C%HMxMQ