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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?
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Assume that one had a piece of paper that was very fine, like the kind they typically use to print the Bible.
聖書に使われているような薄い紙が1枚あったとしましょう
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In reality, it seems like a piece of silk.
実際 シルクのように見えます
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To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness.
計算を進めるため紙の厚さを1000分の1センチとしましょう
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That is ten to the power of minus three centimeters, which equals .001 centimeters.
10のマイナス3乗センチつまり0.001cmです
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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
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Now we begin to fold it in half.
これを半分に折っていくと
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How many times do you think it could be folded like that?
何回折れると思いますか?
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And another question:
もう1つの疑問は
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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?
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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
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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
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If we fold it in half once again, the paper will become four-thousandths of a centimeter.
もう1度半分に折ると1000分の4センチになります
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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
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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
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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
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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?
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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
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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
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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
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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
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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
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What do we learn?
何が分かるでしょう?
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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
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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
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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
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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
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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"
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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
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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