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  • How many times can you fold a piece of paper?

    1枚の紙は 何回 折ることができるでしょう?

  • Assume that one had a piece of paper that was very fine, like the kind they typically use to print the Bible.


  • In reality, it seems like a piece of silk.

    実際 シルクのように見えます

  • To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness.


  • That is ten to the power of minus three centimeters, which equals .001 centimeters.


  • Let's also assume that you have a big piece of paper, like a page out of the newspaper.

    またその紙は 新聞紙のように十分に大きいものとしましょう

  • Now we begin to fold it in half.


  • How many times do you think it could be folded like that?


  • And another question:


  • If you could fold a paper over and over, as many times as you wish, say 30 times, what would you imagine the thickness of the paper would be then?

    紙を好きなだけ何回でも 折っていけるとしたら例えば30回折ったときに その紙の厚さは どのくらいになるでしょう?

  • Before you move on, I encourage you to actually think about a possible answer to this question.

    先に進む前に答えを自分で考えてみるよう おすすめします

  • Okay. After we have folded the paper once, it is now two-thousandths of a centimeter in thickness.

    ではやってみましょう この紙を1回折ると厚さは1000分の2センチになります

  • If we fold it in half once again, the paper will become four-thousandths of a centimeter.


  • With every fold we make, the paper doubles in thickness.

    1回折るごとに 紙の厚さは2倍になります

  • And if we continue to fold it again and again, always in half, we would confront the following situation after ten folds.

    繰り返し半分に 折り続けていくと10回折った後 どうなっているかというと

  • Two to the power of ten, meaning that you multiply two by itself ten times, is one thousand and 24 thousandths of a centimeter, which is a little bit over one centimeter.

    厚さは2の10乗つまり2を10回 掛け合わせたものですが 1000分の1024センチになります 1センチ強です

  • Assume we continue folding the paper in half. What would happen then?

    さらに紙を半分に 折り続けたとしたらどうなるでしょう?

  • If we fold it 17 times, we'll get a thickness of two to the power of 17, which is 131 centimeters, and that equals just over four feet.

    17回折ったところで厚さは2の17乗 つまり131cmになり 4フィートを越えます

  • If we were able to fold it 25 times, then we would get two to the power of 25, which is 33,554 centimeters, just over 1,100 feet.

    25回折ることができたとしたら2の25乗倍の厚さ つまり33,554cmとなり 1,100フィートを 越えてしまいます

  • That would make it almost as tall as the Empire State Building.

    エンパイアステートビルと ほぼ同じ高さです

  • It's worthwhile to stop here and reflect for a moment.

    ちょっと立ち止まって 振り返ってみましょう

  • Folding a paper in half, even a paper as fine as that of the Bible, 25 times would give us a paper almost a quarter of a mile.

    聖書の紙と同じくらい 薄い紙でも25回折ると 厚さが 約 3分の1 kmにもなります

  • What do we learn?


  • This type of growth is called exponential growth, and as you see, just by folding a paper we can go very far, but very fast too.

    このタイプの増え方を 指数的増加といいご覧の通り 紙を折っていくだけで とても早くとても遠くまで行くのです

  • Summarizing, if we fold a paper 25 times, the thickness is almost a quarter of a mile.

    まとめです 紙を25回折ると厚さは約 3分の1 kmになり

  • Thirty times, the thickness reaches 6.5 miles, which is about the average height that planes fly.

    30回で厚さは10 kmに及び飛行機の平均高度と 同じくらいになります

  • Forty times, the thickness is nearly 7,000 miles, or the average GPS satellite's orbit.

    40回で厚さは ほぼ 11,000 kmGPS衛星軌道までの 平均距離になり

  • Forty-eight times, the thickness is way over one million miles.

    48回だと厚さは 何百万kmにもなります"

  • Now, if you think that the distance between the Earth and the Moon is less than 250,000 miles, then starting with a piece of Bible paper and folding it 45 times, we get to the Moon.

    地球と月の間の距離は38万km程度なので 聖書の紙1枚から始めて 45回折ることで 月まで届きます

  • And if we double it one more time, we get back to Earth.

    さらにもう1回折ると地球に戻ってきます 先生: アドリアン・パエンザ ナレーション: アドリアン・パエンザ アニメーション: TED-Edチーム

How many times can you fold a piece of paper?

1枚の紙は 何回 折ることができるでしょう?

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