Name: 【TED-Ed】如何藉紙奔月 (How folding paper can get you to the moon - Adrian Paenza)
Uploaded: 2021-11-20T21:01:30.000Z
Duration: 3 min 49 s

How many times can you fold a piece of paper?

程度副詞

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。

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

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.

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.

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。

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！