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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.

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

• 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.

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

• 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

• 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.

これを半分に折っていくと

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

何回折れると思いますか？

• And another question:

もう１つの疑問は

• 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.

もう１度半分に折ると1000分の4センチになります

• 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?

何が分かるでしょう？

• 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&quot;

• 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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# 【TED-Ed】紙を折って月に行く方法 (How folding paper can get you to the moon - Adrian Paenza)

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Yu Syuan Luo に公開 2013 年 10 月 16 日