triangle

yma16 · 发表于 2005-11-20 01:27:53

Explain why on any surface, there exist 3 points to form a triangle of any given shape. In other words, If you draw a triangle, I can find three points on any surface such the triangle formed by these three points is "similar" to yours. The hard question is to show there exsit 4 points to form a square. The surface could be a handkerchief inside your pocket with holes.

本贴由[husonghu]最后编辑于：2005-11-20 15:1:41

husonghu · 发表于 2005-11-20 23:04:43

yma16，我对你贴修改了一下: hankerchief --> handkerchief

yma16 · 发表于 2005-11-21 02:49:37

Thank you. eom

乱弹 · 发表于 2005-11-21 17:55:18

尤其是那个 square 问题。有一个相关的类似猜想是：在一个平面简单闭曲线上有四个点组成一个正方形。到目前为止还没有完全结论。

随便评论而已。没有时间想，有时间想也想不出来。

yma16 · 发表于 2005-11-21 19:49:39

The triangle one is not hard. Rectangle one needs more explanation. The one you mentioned is a black hole.

乱弹 · 发表于 2005-11-22 06:17:23

Really？ I do not remember you posted it. Maybe you did in August?

You did not mention rectangle in your first post. The square problem is super hard. For the other two problems, I read some articles about it. Probably you have better solutions.

yma16 · 发表于 2005-11-22 16:38:40

square and rectangle should be similar-imo. eom

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triangle

yma16，我对你贴修改了一下: hankerchief --> handkerchief [:)]

Thank you. eom

很有意思的一个问题。最近的很多问题都很有意思。 [>:D<]

I post it at WXC before.

回复：I post it at WXC before.

square and rectangle should be similar-imo. eom