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


  • 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.


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

    為了要把這個想法量化,假設紙的厚度是 1/1000 公分。

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

    也就是 10 的 -3 次方公分,相當於 0.001 公分。

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


  • 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?


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


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

    好,在對摺一次後,厚度變成 2/1000 公分。

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

    如果再對摺一次,這張紙就會變成 4/1000 公分。

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


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


  • 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.

    2 的 10 次方,也就是 2 自乘 10 次,也就是 1024/1000 公分,比 1 公分多一點。

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


  • 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.

    如果對摺 17 次厚度就是 2 的 17 次方,大約是 131 公分,超過 4 英尺(1.3 公尺)。

  • 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.

    如果我們可以對摺 25 次,就會得到 2 的 25 次方,大約 33,554 公分,超過 1100 英尺(335 公尺)。

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


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


  • 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.

    就算紙張跟聖經一樣薄,對摺了25 次後,厚度會接近 1/4 英里。

  • 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.


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

    總之,如果我們將紙對摺 25 次,厚度大約會是 1/4 英里。

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

    30 次的厚度,接近 6.5 英里(10 公里),大約是飛機的平均飛行高度。

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

    40 次的厚度,將近 7,000 英里(一萬公里),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 is less than 250,000 miles, then starting with a piece of Bible paper and folding it 45 times, we get to the Moon.

    你想想,地球到月球的距離還不到 25 萬英里(約 38 萬公里),用一張聖經紙摺 45 次,我們就可以到達月球。

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


How many times can you fold a piece of paper?


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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 2021 年 11 月 20 日