英语翻译

Question

Take any long piece of paper.Now glue the ends of the paper together.You have made a ring.
Take a second long piece of paper,twist the paper once and glue the ends together.Now you have made a Mobius band. For people who study math,this band is special.
This strange band was first made in the 1800s by a German named August Mobius.Mr. Mobius studies math. He wanted to find a way to prove how this band work with math. Believe or not,this band has only one surface. You can find this out for yourself.
If you draw a line on the surface of the paper before,you twist and glue it,the line is only on the side of the paper.The paper has two surfaces.However, if you draw a line after you make the Mobius band,you can follow the line around all sides of the paper.In other words,the Mobius band must have only one surface.
It is also kind of fun to see what happens when you cut the Mobius band in half once down the line you drewn, you do not get two Mobius bands. Instead,after you cut the band,it turns into one large twisted ring.Then,if you cut this ring in half along the middle of the band again,you get two connected Mobius bands.

Answer 1

我试一下，可能不完美，还希望各位朋友指正。

把一条细长的纸用胶水将两端粘紧，你就获得了一个指环。

相同的，把另一条细长的纸扭曲后粘紧两端，你就得到了一个莫比乌斯带。这个带子对学习数学的人来说，是很特别的。

这个神奇的带子于1800年间由一个学习数学的德国人发明，这个人就叫做奥格斯特·莫比乌斯。他试图证明这条带子和数学有着联系。不管你信不信，这条带子只有一表面，并且你可以通过自己的实践证明这一点。

如果在扭曲前，你往一张细长纸的表面上画一条线，这条线只是在纸的一边出现。这张纸有两个表面（正，反两面，译者注）。但是如果你在一个莫比乌斯带上画线的话，你会画在纸的每一面上。换句话说，莫比乌斯带必须只能有一个表面。

还有有趣的事情，如果你沿着你画的线剪开莫比乌斯带的话，它不会变成两个。相反的，它会变成一个扭曲的大指环。 当你从这个大指环一半的地方，沿着中间剪开的话，你会得到两个连在一起的莫比乌斯带。