An acquaintance approached me with the following starter:
"You know, it's interesting what happens when you glue together a paper chain, and then cut it along its center lines..."
and then he demonstrated the effect with two rings. Yes, interesting--the two rings somehow turned into a square...!
Then, we proceeded to contemplate what would happen using more rings.
Later, he demonstrated what happens when using paper chains with 1-8 rings; the results were quite fascinating.
You can see some (Japanese) articles about this effect, by following the top Google search results from the links below--just stare at some of the pictures, and perhaps the video, and you'll probably get the point...
Now, I will try to explain what is happening, in layman's terms.
(I won't try to do the proper Topological analysis here... hopefully someone will fill in)
From here, I will continue on, expecting the reader to have seen the above articles, or have actually tried this out.
[Japanese blog entry equivalent: 輪飾り（輪つなぎ）切断を似非数学的に考えてみる
the Japanese counterpart will probably be ahead of this page in terms of content...]
(UNDER CONSTRUCTION)