国立科学博物館 丸木舟で３万年前の航海再現へ

国立科学博物館

丸木舟で３万年前の航海再現へ

 

国立科学博物館（茨城県つくば市）などは、日本人の祖先が３万年前に大陸からやってきた航海を再現しようと、旧石器時代の道具のみを使った丸木舟の制作を始めた。今月から作業を始め、波の穏やかな湾内での航行実験を経て、２年後に挑む予定の再現航海で使えるかを検証する。

　アフリカから世界に広がったホモ・サピエンス（新人＝今の人類）が日本に来た経過を科学的に検証するプロジェクトの一環。チームは、３万年前に存在していたと考えられる簡単な道具で作れる舟を使って、台湾から沖縄・与那国島まで２００キロ以上の航海を目指している。

　チームは今年６月、台湾に自生する竹を使ったいかだで航行テストを実施した。シーカヤックなどの経験が豊富な５人が乗り込み、台湾南東部の海岸を出発し、５０キロ沖合の離島を目指した。強風と日没で到着目前でのリタイアとなったが、次の挑戦への手応えを感じたという。

　今回は首都大学東京のチームと共同で、旧石器時代にもあった石のおので木を伐採し、くりぬいて丸木舟を作ることができるかを調べる。また縄文時代の丸木舟の復元舟を使い、京都府舞鶴市で実際にこぐ実験も並行して進める。

　プロジェクト代表の海部陽介・同館人類史研究グループ長は「舟の選定と同時に、地図も天気予報も海流予測もない当時の人の航海戦略を検討し、来年には台湾－与那国島間の航海に向けた準備を本格化させたい」と意気込む。【大場あい】https://mainichi.jp/articles/20170921/k00/00e/040/226000c

考古学にとても興味があります：

\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\\

E-mail: kbdmm360@yahoo.co.jp\\

}

\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\\

E-mail: kbdmm360@yahoo.co.jp\\

}

\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}