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.
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.
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.
Suppose that you start with an standard A4 sheet of paper - about 300 mm long, and about 0.05 mm thick.
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.
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.
In fact, if you had a sheet of paper, and folded it in half 50 times, how thick would it be?
The answer is about 100 million kilometres, which is about two thirds of the distance between the Sun and the Earth.
And so Accepted Wisdom on Paper-Folding ruled, until 2001.
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.
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.
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.
2010-08-10 23:39 编辑：kuaileyingyu