Exponential Growth: How folding paper can get you to moon


 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 the idea, let's say you have a paper that is one thousandth of a centimetre in thickness. That is 10 to the power of minus three centimetres, which equals 0.01 cementers. Let's also assume that you have a big piece of paper, Like a page out of a 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 the paper over and over, as many times as you wish, say 30 times, what would you imagine the thickness of paper would be then? Before you move on, I encourage you to actually think about a possible answer to this question. After you have folded the paper once, it is now two thousand of centimetre in thickness.. With every fold we make , the paper doubles its thickness. And if we continue to fold it again and again, always in half, we would confront the following situation after 10 folds. Two to power of 10 meaning that you multiply two by itself 10 times, is one thousand and  24 thousandths of a centimetre, which is a little bit over 1 cm. Assume we continue folding the paper in half, What will happen then?

     If we fold it 17 times, we will get thickness of two to power of 17, which is 131 centimetres, and that equals just over 4 feet. If we were able to fold it 25 times, then we would get 33,554 cm, 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 Bible, 25 times would give us 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 miles, 40 times, the thickness is nearly 7,000 miles, or the average GPS satellite's orbit. And folding it 45 times, we get to moon, and if we double it one more time we get back to earth.

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