I've written a document describing how the "Haberdasher Puzzle" was only apparently solved by "Dudeney's Dissection". This is a puzzle from 1902 where you are asked to transform an equilateral triangle into a perfect square.
EDIT: Ah, I finally figured out my mistake. Now I can see where I went wrong. I'll edit my document & republish soon.
See http://blog.makezine.com/archive/2009/09/dudeneys_dissection.html for the link that started me down this path. Googling the above quoted terms also turns up many interesting links.