## 字幕表 動画を再生する

• (Music)

(音楽)

• 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,

聖書に使われているような

• like the kind they typically use to print the Bible.

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,

計算を進めるため

• let's say you have a paper that's one-thousandth of a centimeter in thickness.

紙の厚さを1000分の1センチとしましょう

• That is 10 to the power of minus three centimeters,

10のマイナス３乗センチ

• which equals .001 centimeters.

つまり0.001cmです

• Let's also assume that you have a big piece of paper,

またその紙は 新聞紙のように

• like a page out of the newspaper.

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,

紙を好きなだけ何回でも 折っていけるとしたら

• say 30 times, what would you imagine the thickness of the paper would be then?

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,

先に進む前に

• I encourage you to actually think about a possible answer to this question.

答えを自分で考えてみるよう おすすめします

• OK. After we have folded the paper once,

ではやってみましょう この紙を１回折ると

• It is now two-thousandths of a centimeter in thickness.

厚さは1000分の2センチになります

• If we fold it in half once again,

もう１度半分に折ると

• the paper will become four-thousandths of a centimeter.

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,

繰り返し半分に 折り続けていくと

• always in half, we would confront the following situation

10回折った後

• after 10 folds.

どうなっているかというと

• Two to the power of 10,

厚さは２の10乗

• meaning that you multiply two by itself 10 times,

つまり２を10回 掛け合わせたものですが

• is one thousand and 24 thousandths of a centimeter,

1000分の1024センチになります

• which is a little bit over one centimeter.

1センチ強です

• Assume we continue folding the paper in half.

さらに紙を半分に 折り続けたとしたら

• What will happen then?

どうなるでしょう？

• If we fold it 17 times,

17回折ったところで

• we'll get a thickness of two to the power of 17,

厚さは２の17乗

• which is 131 centimeters,

つまり131cmになり

• and that equals just over four feet.

４フィートを越えます

• If we were able to fold it 25 times,

25回折ることができたとしたら

• then we would get two to the power of 25,

２の25乗倍の厚さ

• which is 33, 554 centimeters,

つまり33,554cmとなり

• just over 1,100 feet.

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,

聖書の紙と同じくらい 薄い紙でも

• 25 times would give us a paper almost a quarter of a mile.

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,

このタイプの増え方を 指数的増加といい

• and as you see, just by folding a paper

ご覧の通り 紙を折っていくだけで

• we can go very far, but very fast too.

とても早くとても遠くまで行くのです

• Summarizing, if we fold a paper

まとめです 紙を25回折ると

• 25 times, the thickness is almost a quarter of a mile.

厚さは約 3分の1 kmになり

• Thirty times, the thickness reaches 6.5 miles,

30回で厚さは10 kmに及び

• which is about the average height that planes fly.

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,

40回で厚さは ほぼ 11,000 km

• or the average GPS satellite's orbit.

GPS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

地球と月の間の距離は

• is less than 250,000 miles,

38万km程度なので

• then starting with a piece of Bible paper

聖書の紙１枚から始めて

• and folding it 45 times, we get to the Moon.

45回折ることで 月まで届きます

• And if we double it one more time,

さらにもう１回折ると

• we get back to Earth.

地球に戻ってきます

• Lesson By : Adrian Paenza narration By : Adrian Paenza Animation by : TED-ED Team

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

(Music)

(音楽)

B1 中級 日本語 TED-Ed 折る 折っ km 半分 折り