## 字幕列表 影片播放

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

假設有一張很薄很薄的紙，像是印聖經的那種紙。

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

實際上，它就像是一片絲綢那麼薄。

• 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.

再假設這張紙夠大，像報紙那麼大。

• Now we begin to fold it in half.

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

如果你能將一張紙任意折疊多次，例如三十次，紙會有多厚？

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

在開始之前，請你好好想想這問題可能的答案。

• 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.

每摺一次，紙張厚度加倍。

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

如果我們不斷對摺十次以後，它就會看起來像這樣。

• 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?

如果我們繼續對摺，會發生什麼事？

• 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.

差不多跟帝國大廈一樣高。

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

現在很值得停下來思考一下。

• 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?

我們學到什麼？

• 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.

這樣的成長稱作「指數型成長」，就如你所看到的，只是把紙對摺就會變得很厚，而且變厚得很快。

• 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.

如果再多摺一次，我們就可以回到地球了！

How many times can you fold a piece of paper?

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