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怎样将一张纸折叠12次

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当我的儿子临近小学毕业时,我想是时候将我怪异又很有趣的科学智慧传授给他了。
When my son was near the end of his primary school years, I thought that it was time that I should impart some of my Weird Freaky Science Wisdom - and have a little bit of fun as well.
我对他说,如果你能将一张纸折叠十次,我就给你一百万。当然他失败了。我知道一定会这样,谁都知道一张纸没有办法被折十次(或者八次,七次)。我告诉他,即使给他一张足球场大小的纸,也是不可能成功的。但是,现在,我知道我错了。
I told him that I would give him a million dollars if he could fold a piece of paper in half, and in half again, and so on for a total of 10 times. Of course he tried, and of course he failed.
建议你用一张A4纸,大约300mm长,0.05mm厚。
I knew that this would happen, because it was "Accepted Wisdom" that it was impossible to fold a piece of paper in half 10 times (or seven, or nine, for that matter.). I told him that it couldn't be done, even if he used paper the size of a football field. But I now know that I was wrong.
第一次折叠后,它会变成150mm长,0.1mm厚。第二次,75mm长,0.2mm厚。等到了第8次(如果你能达到),你会得到一坨1.25mm长,但有12.8mm那么厚的纸。它的厚度比长度长得多,想再折一次比折叠成品钢还难。
Suppose that you start with an standard A4 sheet of paper - about 300 mm long, and about 0.05 mm thick.
在网络上一般的表述是,“无论一张多大多薄的纸,都无法被折叠七次”,而且当你眼神幽怨的看着自己的那一坨,你就会相信了。
The first time you fold it in half, it becomes 150 mm long and 0.1 mm thick. The second fold takes it to 75 mm long and 0.2 mm thick. By the 8th fold (if you can get there), you have a blob of paper 1.25 mm long, but 12.8 mm thick. It's now thicker than it is long, and, if you're trying to bend it, seems to have the structural integrity of steel.
如果你折叠五十次,你会得到一坨厚度为一亿公里的纸,大约是太阳到地球距离的三分之二。因此就有了折纸定律,直到2001年。
A typical claim on the Internet might run, "No matter its size or thickness, no piece of paper can be folded in half more than 7 times", and as you stare sadly at your block of folded paper, you tend to agree.
那一年高中生Britney Gallivan获得一个数学问题。如果她能选择合适的纸张,将其折叠十二次,她就能得到额外的数学学分。她在正常尺寸纸张的寻找中失败了。但是她聪明的找到了一种特别薄的东西——金箔,只有一米的百万分之0.28那么厚。她使用一个10cm见方的金箔,在尺子,油漆刷,小镊子的帮助下成功将其折叠了12次。但是他的数学老师说,用金箔来得太简单了,她必须将一张纸折叠12次。
In fact, if you had a sheet of paper, and folded it in half 50 times, how thick would it be?
Britney Gallivan继续研究这个问题,并找到了两种数学上的解决方案。第一种方案是在常规模式下折纸,不断交替变换折叠的方向。她推导出了一个关于折叠次数(n)、宽度(w)和材料厚度(t)关系的方程
The answer is about 100 million kilometres, which is about two thirds of the distance between the Sun and the Earth.
第二种方案是将纸按一个方向折叠,就是折叠一张长但窄的纸。她推导出了另一个关于折叠次数(n)、现实的最小长度(l)以及材料厚度(t)的关系式。
And so Accepted Wisdom on Paper-Folding ruled, until 2001.
她仔细研究发现,如果你想折叠一张纸很多次,最好找一张长但窄的纸。她的公式告诉她,如果想要成功的将一张纸折叠12次,需要这张纸达到1.2千米那么长。最终,她找到了一种特殊的能满足她的要求的厕纸,价值85美元。
That was when a high school student, Britney Gallivan (of Pomona, California) was given a maths problem. She would get an extra maths credit, if she took up the option of solving the problem of folding a sheet in half 12 times. She tried and failed with reasonably-sized sheets of paper.
在2002年1月,在父母的陪同下,Britney Gallivan进入了位于Pomona的大型购物中心。铺开那卷庞大的厕纸,开始了第一次折叠。由于太长,用了一段时间才完成。然后她继续折叠第二次……第三次……第四次……
So she got smart, and used something incredibly thin - gold foil, only 0.28 of millionth of a metre thick. She started with a square sheet, 10 cm by 10 cm. It took lots of determination and practice, as well as rulers, soft paint brushes and tweezers, but she finally succeeded in folding her gold foil in half 12 times. She ended up with a microscopic square sheet of gold foil.
七个小时后,她将她的纸折成了一个80CM长,40cm高的紧梆梆的厚板,折叠了11次。她再一次折叠它,并将她的成功写入了她40页的小册子《怎样将一张纸折叠12次:一个不可能完成的挑战的解决方法》,,她在这本小册子上写到,“当我完成那第12次折叠的时候,世界是那么美丽”。
But her maths teacher said that ultra-thin gold foil was too easy - she had to fold paper 12 times.
就像西班牙诗人、1956年诺贝尔文学奖获得者Juan Ramon所说的那样,Britney Gallivan的成功是因为其的反抗精神和坚定的决心。人类的质疑以及永不妥协的精神,“如果他们给一纸禁令,那就换一种方式来书写。”
She studied the problem, and came with two mathematical solutions.
标签:折叠
1880
2010-08-10 23:39 编辑:kuaileyingyu
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