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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.

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

• 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.

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

• 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.

• 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.

• 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.

• 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.

• 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.

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

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

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

• 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.

• 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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# 【TED-Ed】How folding paper can get you to the moon - Adrian Paenza

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Yu Syuan Luo posted on 2021/11/20
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