折纸与指数增长

折纸，听起来很简单，对嘛？

2011年，美国德克萨斯州圣马克中学师生们把长达 $4$ 公里的厕纸对折了 $13$ 次——2002年，9年前，这个记录是 $12$ 次。

现场视频，跳转到搜狐观看

理论上，一张纸可以被无限折叠下去。实际上，折叠次数多了，纸张的内外受力会不均匀，导致纸张弹开，难以继续折叠。

以下是理论计算：

一张 $0.01$ mm， $1.0000\times 10^{-5}$ 米的纸

对折 $3$ 次，厚 $8.0000\times 10^{-5}$ 米

对折 $10$ 次，厚 $1.0240\times 10^{-2}$ 米

对折 $25$ 次，厚 $3.3554\times 10^2$ 米

对折 $30$ 次，厚 $1.0737\times 10^4$ 米， $10.737$ 千米

对折 $40$ 次，厚 $1.0995\times 10^7$ 米， $10995$ 千米

对折 $80$ 次，厚 $1.2089\times 10^{19}$ 米， $1281$ 万光年

对折 $100$ 次，厚 $1.2676\times 10^{25}$ 米， $1.34$ 亿光年

如果对折 $110$ 次，就厚 $1.2981\times 10^{28}$ 米， $1370$ 亿光年！而目前测得的宇宙直径，为 $920$ 亿光年！

折纸 $110$ 次，你就是宇宙的神！

指数增长威力巨大，你是否要试试？

最后附上计算程序源代码：

#include<iostream>
using namespace std;
int main(){
  int a;              \\折叠次数
  float b=0.00001     \\单张纸厚度（米）
  cin>>a;
  for(int i=1;i<=a;i++) b*=2;
  cout<<b;
  return 0;
}

It sounds easy to fold paper, right?

In 2011, about $4$ km of toliet paper was folded $13$ times by teachers and students in St. Mark’s School Of Texas, USA. The record was still $12$ times 9 years ago, in 2002.

In theory(理论), a piece of paper can be folded infinitely(无限地). But in fact, if we fold the paper for many times, the stresses between each side of the paper are different, so we cannot keep folding a piece of paper forever.

Here are theoretical calculations(理论计算)

A piece of $0.01$ mm, $1.0000\times 10^{-5}$ m paper,

If we fold $3$ times, it will be $8.0000\times 10^{-5}$ m;

If we fold $10$ times, it will be $1.0240\times 10^{-2}$ m;

If we fold $25$ times, it will be $3.3554\times 10^2$ m;

If we fold $30$ times, it will be $1.0737\times 10^4$ m, that is $10.737$ km;

If we fold $40$ times, it will be $1.0995\times 10^7$ m, that is $10995$ km;

If we fold $80$ times, it will be $1.2089\times 10^{19}$ m, that is $12.81$ millon light years;

If we fold $100$ times, it will be $1.2676\times 10^{25}$ m, that is $1.34$ hundred millon light years;

And if we fold $110$ times, it will be $1.2981\times 10^{28}$ m, that is $1370$ hundred millon light years! Until now, as human’s knowledge, the length of space, is $920$ hundred millon light years!

If you fold a piece of paper for $110$ times, you will be the god of space.

Exponential growth(指数增长) has a great power, do you want to try?