甜甜按:这篇文章比那篇叫做“世界上最难的简单几何体”的文章简单多了。虽则如此,翻译它还是花费了我一些时间,翻译出来的东西还是怪怪的。学习好的人可以先看一下英文。或者去头脑风暴网http://thinkzone.wlonk.com/index.htm
否则,可以去下面看译文。
Four Color Map Puzzle
The four color theorem says that you only need four colors to color any normal map so that no bordering regions have the same color. The proof was so hard it required a computer. Can you color this blank map using only four colors? Try it before you look at the solution (by clicking the image). Puzzle from Martin Gardner.
Möbius Strip
Make a Möbius strip by taking a strip of paper, giving it a half twist, and taping the ends together. Now cut it in half the long way. It's surprising. Make another Möbius strip and cut it in thirds the long way. It's also surprising. Try different numbers of twists and different numbers of cuts.
Turning a Sphere Inside-out
Can you smoothly turn a sphere inside-out, conceptually allowing the surface to intersect itself, but never allowing any sharp creases? Steve Smale proved it could be done. Bill Thurston invented this non-optimal but very beautiful method. These images are from the animation
http://www.geom.uiuc.edu/docs/outreach/oi/ , copyright © http://www.geom.uiuc.edu/ .
译文:
(1)四色问题
四色猜想认为涂满一张普通地图只需要四种颜色,使得任意两个接触的地区颜色都不同。证明它实在太难了,只好弄了一台电子计算机来。你能用四种颜色涂满上面的空白地图么?点击图片看答案
(简单学习论坛的系统没这么高级——甜甜注)之前先试试吧。四色问题是由马丁·加德纳提出来的。
(2)莫比乌斯环
制作莫比乌斯环的方法是弄一条纸带,扭一下,首尾相接。现在把它从中间剪开。会出现一个奇怪的现象
(纸圈不会一分为二,而是变为一个更大的纸圈——甜甜注)。再做一个莫比乌斯环,把它从三等分处剪开。又会出现一个奇怪的现象
(纸圈会变为一个较大的和一个较小的套在一起——甜甜注)。试着从不同的地方剪开,剪不同的次数。
(3)使球内面向外
你能顺利地使一个球内面向外,使它的表面变为它的里面,而又不使任何地方变皱么?史蒂夫·斯麦尔证明了这是可行的。比尔·瑟斯顿发明了这个“非政治性的”
(这个词很难找到另一个解释——甜甜注)但是很漂亮的方法。图片来自:"彻底了结"动画制作公司,“几何中心”公司与明尼苏达大学权利保留。
(为了尊重原作者,原文中没有去掉外链——甜甜注)