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

    一張紙可以對摺幾次?

  • Assume that one had a piece of paper that was very fine,

    假設有一張很薄很薄的紙

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

    像是印聖經的那種紙

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

    實際上,就像是一根絲那麼薄

  • To qualify these ideas,

    為了要把這個想法量化

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

    假設紙的厚度是 1/1000 公分

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

    也就是 10 的 -3 次方公分

  • which equals .001 centimeters.

    相當於 0.001 公分

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

    再假設這張紙夠大

  • like a page out of the newspaper.

    像報紙那麼大

  • Now we begin to fold it in half.

    我們開始將它對摺

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

    你覺得我們可以對摺幾次?

  • And another question:

    另一個問題是:

  • If you could fold a paper over and over, as many times as you wish,

    如果你能將一張紙 折疊任意多次

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

    比方說 30 次 你想那時紙會有多厚?

  • Before you move on,

    在開始之前

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

    我鼓勵你好好想想 這問題可能的答案

  • OK. After we have folded the paper once,

    好,在對摺一次後

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

    厚度變成 2/1000 公分

  • If we fold it in half once again,

    如果再對摺一次

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

    這張紙就會變成 4/1000 公分

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

    每摺一次,紙張厚度加倍

  • And if we continue to fold it again and again,

    如果我們不斷對摺

  • always in half, we would confront the following situation

    十次以後

  • after 10 folds.

    我們就會見到這種情景

  • Two to the power of 10,

    2 的 10 次方

  • meaning that you multiply two by itself 10 times,

    也就是將 2 自乘 10 次

  • is one thousand and 24 thousandths of a centimeter,

    就是 1024/1000 公分

  • which is a little bit over one centimeter.

    比 1 公分多一點

  • Assume we continue folding the paper in half.

    如果我們繼續對摺

  • What will happen then?

    會發生什麼事?

  • If we fold it 17 times,

    如果對摺 17 次

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

    厚度就是 2 的 17 次方

  • which is 131 centimeters,

    大約 131 公分

  • and that equals just over four feet.

    超過 4 英尺 (1.3 公尺)

  • If we were able to fold it 25 times,

    如果我們可以對摺 25 次

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

    就會得到 2 的 25 次方

  • which is 33, 554 centimeters,

    大約 33,554 公分

  • just over 1,100 feet.

    超過 1100 英尺 (335 公尺)

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

    差不多跟帝國大廈一樣高

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

    現在很值得停下來反思一下

  • Folding a paper in half, even a paper as fine as that of the Bible,

    就算紙張跟聖經一樣薄,對摺了

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

    25 次後,厚度會接近 1/4 英里

  • What do we learn?

    我們學到什麼?

  • This type of growth is called exponential growth,

    這樣的成長稱作「指數型成長」

  • and as you see, just by folding a paper

    就如你所看到的,只是把紙對摺

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

    就會變得很厚,而且變厚得很快

  • Summarizing, if we fold a paper

    總之,如果我們將紙對摺 25 次

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

    厚度大約是 1/4 英里

  • Thirty times, the thickness reaches 6.5 miles,

    30 次的厚度,接近 6.5 英里 (10 公里)

  • which is about the average height that planes fly.

    大約是飛機的平均飛行高度

  • Forty times, the thickness is nearly 7,000 miles,

    40 次的厚度,將近 7,000 英里 (一萬公里)

  • or the average GPS satellite's orbit.

    是 GPS 衛星軌道 平均高度的一半

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

    摺 48 次,厚度就超過一百萬英里 (280 萬公里)

  • Now, if you think that the distance between the Earth and the Moon

    你想想,地球到月球的距離

  • is less than 250,000 miles,

    還不到 25 萬英里 (約 38 萬公里)

  • then starting with a piece of Bible paper

    用一張聖經紙

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

    摺 45 次,我們就可以到達月球

  • And if we double it one more time,

    如果再多摺一次

  • we get back to Earth.

    我們就可以回到地球了!

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

    課程: Adrian Paenza 講解: Adrian Paenza 動畫: TED-ED 團隊

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B1 中級 中文 TED-Ed 次方 紙張 假設 聖經 月球

【TED-Ed】如何藉紙奔月 (How folding paper can get you to the moon - Adrian Paenza)

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    Yu Syuan Luo 發佈於 2013 年 10 月 16 日
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