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折纸带你去月球

How Folding Paper Can Get You to the Moon

你能将一张纸折上多少次?
How many times can you fold a piece of paper?
假设某人有一张很好的纸,
Assume that one had a piece of paper that was very fine,
就像印刷圣经的那种。
like the kind they typically use to print the Bible.
实际上,它看上去像一块丝绸。
In reality, it seems like a piece of silk.
为了符合这个想法,
To qualify these ideas,
假定你有一张纸,
let’s say you have a paper
它的厚度是千分之一厘米。
that’s one-thousandth of a centimeter in thickness.
折三厘米厚纸的力气是
That is 10 to the power of minus three centimeters,
三厘米纸张的十倍。
which equals .001 centimeters.
继续假设你有一大张纸,
Let’s also assume that you have a big piece of paper,
就像一大张报纸。
like a page out of the newspaper.
现在开始对折。
Now we begin to fold it in half.
你认为我们能这样重复多少次呢?
How many times do you think it could be folded like that?
另外一个问题:
And another question:
如果你能一直折下去,就像你希望的那样,
If you could fold the paper over and over, as many times as you wish,
30次,
say 30 times,
你能想象折的有多厚吗?
what would you imagine the thickness of the paper would be then?
在你行动之前,
Before you move on,
我建议你按照实际考虑下问题答案的可能性。
I encourage you to actually think about a possible answer to this question.
好的。
OK.
在你第一次折纸前,
After we have folded the paper once,
这是两千分之一厘米的厚度。
it is now two thousandths of a centimeter in thickness.
如果我们再来一次,
If we fold it in half once again,
厚度变成了两千分之四厘米。
the paper will become four thousandths of a centimeter.
每折一次,纸的厚度就变成了双倍厚。
With every fold we make, the paper doubles in thickness.
如果我们一直折下去,
And if we continue to fold it again and again,
一直对折,我们将面对以下这种情况,
always in half, we would confront the following situation
十次之后,
after 10 folds.
2 ^10次
Two to the power of 10,
意味着你把这两者想乘十次,
meaning that you multiply two by itself 10 times,
是1000又24/1000厘米,
is one thousand and 24 thousandths of a centimeter,
超过1厘米一点点。
which is a little bit over one centimeter.
假设我们继续折纸的一半。
Assume we continue folding the paper in half.
将会发生什么呢?
What will happen then?
如果對摺 17 次
If we fold it 17 times,
厚度就是 2 的 17 次方
we’ll get a thickness of two to the power of 17,
是131厘米,
which is 131 centimeters,
刚好超过4英尺。
and that equals just over four feet.
如果我们能折25次,
If we were able to fold it 25 times,
就會得到 2 的 25 次方
then we would get two to the power of 25,
33554厘米,
which is 33,554 centimeters,
刚好超过1000英尺。
just over 1,100 feet.
这几乎和纽约帝国大厦一样高。
That would make it almost as tall as the Empire State Building.
是时候停下来思考一下了。
It’s worthwhile to stop here and reflect for a moment.
把纸对折,哪怕这纸跟圣经一样的好,
Folding a paper in half, even a paper as fine as that of the Bible,
25次的对折相当于1.25英里。
25 times would give us a paper almost a quarter of a mile.
我们从中学到了什么呢?
What do we learn?
这种类型的增长方式被称为指数增长,
This type of growth is called exponential growth,
就像你所看到的那样,
and as you see, just by folding a paper
我们能够得到和数值增长一样快的厚度.
we can go very far, but very fast too.
总的来说,如果我们可以把一张纸对折25次,
Summarizing, if we fold a paper 25 times,
这张纸的厚度差不多等于1/4英里.
the thickness is almost a quarter of a mile.
对折30次,厚度将达到6.5英里,
30 times, the thickness reaches 6.5 miles,
这个数值已经达到飞机飞行的平均高度了.
which is about the average height that planes fly.
对折40次,厚度差不多有7000英里,
40 times, the thickness is nearly 7,000 miles,
这是GPS卫星轨道的高度了.
or the average GPS satellite’s orbit.
对折48次,厚度将超过一百万英里.
48 times, the thickness is way over one million miles.
现在,如果你想起地球和月球之间的距离你会发现
Now, if you think that the distance between the Earth and the Moon
也就25万英里不到,
is less than 250,000 miles,
然后我们开始折叠一页圣经纸
then starting with a piece of Bible paper
对折45次,我们就可以用它碰到月球.
and folding it 45 times, we get to the Moon.
如果我们重复一次的话,
And if we double it one more time,
我们能回到月球。
we get back to Earth.

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