平城京にペルシャ人の役人がいたことが判明。「破斯清通」ってどんな人？
奈良市の平城宮跡で出土した木簡に、ペルシャ人の役人とみられる「破斯清通（はしのきよみち）」という名前が記されていたことが10月5日、奈良文化財研究所（奈文研）の調査でわかった。
奈文研によると、国内の出土品でペルシャ人を示す文字が確認されたのは初めて。「破斯（はし）」は「ペルシャ（現在のイラン付近）」を意味する。外国人が来日し、国際色豊かだった平城京の姿を知る史料になりそうだ。
ハフポスト日本版では奈文研・史料研究室の渡辺晃宏・室長に詳しい話を聞いた。
――この木簡は、いつごろ発見されたのでしょうか？
1966年8月に、平城宮跡・東南隅の築地塀の「雨落ち溝」で出土しました。1万3000点の木簡が出土しましたが、「破斯」の文字があった木簡はそのうちの1枚です。長さ268mm、幅32mm、厚さは最も厚みがある箇所で3mmです。腐食している箇所がありますが、四角い木の板だと思っていただければと。
――木簡にはどんな内容が記されていましたか？
書かれていたのは「大学寮解 申宿直官人事 員外大属破斯清通 天平神護元年」の文字です。「天平神護元年」は西暦765年で、聖武天皇の娘だった孝謙天皇が、再び皇位に就いて「称徳天皇」となっていた時代ですね。
記されていた内容は、役人を養成する「大学寮」の宿直勤務の記録です。「大属（だいさかん）」は役職名で、四等事務官にあたります。「員外」は特別職の意。おそらくこのペルシャ人の学問的知識を活かすため、特別枠で任命されたのだと思います。ただ、宿直の勤務にも従事していたということは、「員外」であっても他の役人と同じように勤務していたと思われます。
――765年ということは、ペルシャ地域がイスラーム勢力（アッバース朝）の支配下にあった時期ですね。「シルクロード」を通り、日本にやってきたということでしょうか。
そうなりますね。この時代の人はペルシャから中国を経由し、それから日本にやってきたのではないでしょうか。
――平安時代に編纂された歴史書『続日本紀』には、天平8年（736年）に「唐の人三人、波斯一人」が聖武天皇に謁見したという記録がありますが、それと関連はありますか？
遣唐使が連れ帰った波斯人のことですね。この人物は、『続日本紀』には李密翳（り・みつえい）という中国名で記されていますが、この記録以後の足取りは不明でした。
李が聖武天皇に謁見したのと、破斯清通の名が木簡に記された時代は30年しか離れていない。破斯清通が、李密翳やその関係者である可能性は十分考えられると思います。
――奈良時代のペルシャ人について知るきっかけになりそうな、ロマンあふれる発見ですね。
わずか2文字の発見ですが、これこそ「偶然のしからしむるところ」ですね。聖武天皇は、唐（中国）と仏教の影響を受けて、国際色豊かな国を目指していました。娘の孝謙天皇（称徳天皇）も西大寺の建立を発願するなど、親の時代同様に国際色豊かな文化を継続させようとしていたのではないでしょうか。その一端を知るきっかけになればと思います。http://www.huffingtonpost.jp/2016/10/05/nara-heijyou-kyu-persia_n_12349792.html?utm_hp_ref=japan
とても興味深い
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\title{\bf Announcement 213: An interpretation of the identity $ 0.999999...... =1$
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
\date{}
\maketitle
{\bf Abstract: } In this announcement, we shall give a very simple interpretation for the identity: $ 0.999999......=1$.
\bigskip
\section{ Introduction}
On January 8, 2008, Yuusuke Maede, 8 years old boy, asked the question, at Gunma University, that (Announcement 9(2007/9/1): Education for genius boys and girls):
What does it mean by the identity:
$$
0.999999......=1?
$$
at the same time, he said: I am most interesting in the structure of large prime numbers. Then, a teacher answered for the question by the popular reason based on the convergence of the series: $0.9, 0.99, 0.999,... $. Its answer seems to be not suitable for the 8 years old boy with his parents (not mathematicians). Our answer seems to have a general interest, and after then, such our answer has not been heard from many mathematicians, indeed.
This is why writting this announcement.
\medskip
\bigskip
\section{An interpretation}
\medskip
In order to see the essence, we shall consider the simplist case:
\begin{equation}
\frac{1}{2} + \frac{1}{2^2} + \frac{1}{2^3} + ... = 1.
\end{equation}
Imagine a tape of one meter length, we will give its half tape: that is,
\begin{equation}
\frac{1}{2}.
\end{equation}
Next, we will give its (the rest's half) half tape; that is, $\frac{1}{2}\cdot \frac{1}{2} = \frac{1}{2^2}$, then you have, altogether
\begin{equation}
\frac{1}{2} + \frac{1}{2^2} .
\end{equation}
Next, we will give the last one's half (the rest's half); that is, $\frac{1}{2}\cdot \frac{1}{2} \cdot \frac{1}{2}= \frac{1}{2^3}$,
then, you have, altogether
\begin{equation}
\frac{1}{2} + \frac{1}{2^2} + \frac{1}{2^3}.
\end{equation}
By this procedure, you will be able to obtain the small tapes endressly. Imagine all the sum as in the left hand side of (2.1). However, we will see that this sum is just the division of the one meter tape. Therefore, we will be able to confim the identity (2.1), clearly.
The question proposed by Y. Maede is just the small change the ratio $\frac{1}{2}$ by $\frac{9}{10}$.
\bigskip
\section{ Conclusion}
Y. Maede asked the true sense of the limit in the series:
$$
0.999999.....
$$
that is, this series is approaching to 1; however, is it equal or not ? The above interpretation means that the infinite series equals to one and it is just the infinite division of one. By this inverse approarch, the question will make clear.
\medskip
\bigskip
\section{Remarks}
Y. Maede stated a conjecture that for any prime number $p$ $( p \geqq 7)$, for $1$ of $ - 1$
\begin{equation}
11111111111
\end{equation}
may be divided by $p$ (2011.2.6.12:00 at University of Aveiro, by skype)
\medskip
(No.81, May 2012(pdf 432kb)
www.jams.or.jp/kaiho/kaiho-81.pdf).
\medskip
This conjecture was proved by Professors L. Castro and Y. Sawano,
independently. Y. Maede gave later an interesting interpretation for his conjecture.
\medskip
(2015.2.26)
\end{document}
\title{\bf Announcement 214: Surprising mathematical feelings of a 7 years old girl
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
\date{}
\maketitle
{\bf Abstract: } In this announcement, we shall give the two surprising mathematical feelings of 7 years old girl Eko Michiwaki who stated the division by 3 of any angle and the division by zero $100/0=0$ as clear and trivial ones. As well-known, these famous problems are historical, and her results will be quite original.
\bigskip
\section{ Introduction}
We had met, 7 years old girl, Eko Michiwaki on November 23, 2014 at Tokyo Institute of Technology and August 23, 2014 at Kusatu Seminor House, with our colleagues. She, surprisingly enough, stated there repeatedly the division by 3 of any angle and the division by zero $100/0=0$ as clear and trivial ones. As well-known, these famous problems are historical and her results will be quite original.
\section{The division of any angle by 3}
\medskip
Eko Michiwaki said:
divide a given angle with 4 equal angles; this is simly done. Next, we divide one divided angle
with 4 equal angles similarly and the three angles add to other 3 angles. By continuing this procedure, we will be able to obtain the division by 3 of any angle. Her idea may be stated mathematically as follows:
$$
\frac{1}{4} + \frac{1}{4^2} + \frac{1}{4^3} + ... ...= \frac{1}{3}.
$$
However, her idea seems to be more clear than the above mathematical formula. For this sentence, see \cite{ann3} for the sense of the limit.
\bigskip
\section{The division by zero $100/0=0$}
\medskip
As we stated in \cite{ann1}, she stated that division by zero $100/0=0$ is clear and trivial for our recent results \cite{cs,kmsy,s,ttk}. The basic important viewpoint is that division and product are different concepts and the division by zero $100/0=0$ is clear and trivial from the own sense of the division, independently of product \cite{ann1}. From the viewpoint, our colleagues stated as follows:
\medskip
On July 11, 2014, Seiichi Koshiba and Masami Yamane said at
Gunma University:
The idea for the division of Hiroshi Michiwaki and Eko Michiwaki (6 years
old daughter) is that division and product are different concepts and they
were calculated independently for long old years, by repeated addition and
subtraction, respectively. Mathematicians made the serious mistake for very
long years that the division by zero is impossible by considering that division
is the inverse operation of product. The division by zero was, however, clear
and trivial, as z/0=0, from the own nature of division.
\medskip
On February 21, 2015, Seiichi Koshiba and Masami Yamane visited our Institute and we confirmed this meaning of these sentences and the basic idea on the division by zero.
\medskip
(2015.2.27)
\bigskip
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{cs}
L. P. Castro and S.Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. Vol. 27, No 2 (2014), pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{s}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances inLinear Algebra \& Matrix Theory. Vol.4 No.2 (2014), 87-95.http://www.scirp.org/journal/ALAMT/
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics (in press).
\bibitem{ann1}
Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics,
Institute of Reproducing Kernels, 2014.10.22.
\bibitem{ann2}
Announcement 185: The importance of the division by zero $z/0=0$, Institute of Reproducing Kernels, 2014.11.28.
\bibitem{ann3}
Announcement 213: An interpretation of the identity $ 0.999999...... =1$, Institute of Reproducing Kernels, 2015.2.26.
\end{thebibliography}
\end{document}
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