６千年前のワインの痕跡、シチリア島の洞窟で発見

（ＣＮＮ） イタリアのシチリア島でこのほど、洞窟から発掘された古代の陶器の中から６０００年前のワインの痕跡が見つかった。研究チームでは、同地のワイン醸造の歴史を塗り替える可能性もある発見と位置付けている。

これまで同地のワイン醸造は、紀元前１３００～１１００年ごろの青銅器時代中期に発達したと考えられていた。しかし今回発見されたワインの痕跡は、その時代を３０００年もさかのぼる。

この研究結果は米南フロリダ大学やイタリア・カターニア大学などの国際研究チームが微量化学の学術誌に発表した。

陶器は銅器時代のもので、シチリア島南西部の沿岸にある洞窟から発掘され、研究チームが容器に残っていた物質の成分を分析した。その結果、ブドウからワインを醸造する過程で発生する酒石酸とナトリウム塩の痕跡が見つかり、同地のワイン醸造は紀元前４０００年ごろから始まっていた可能性があることが分かった。

発見場所の洞窟は、古代の宗教行事に使われていたことも分かっているといい、ワインは地下の神々への供え物だったのではないかと研究者は推測。「考古学的にも歴史的にも重要な発見」と解説している。

研究チームでは今後、陶器の中のワインが赤だったのか白だったのかを解明したい意向。https://www.cnn.co.jp/fringe/35106580.html?tag=cbox;fringe

考古学にとても興味があります：

Announcement 213: An interpretation of the identity $ 0.999999...... =1$

カテゴリ：カテゴリ未分類

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\begin{document}

\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}

Announcement 214: Surprising mathematical feelings of a 7 years old girl

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\numberwithin{equation}{section}

\begin{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}