I Has A Theorem...

[anicca]

Someone tell me if this already exists.

You have two squares with one common corner, lets call them ACBD and DEFG. If a square is constructed with C and E (the corners of each square that are nearest to each other) at opposite corners, the third corner of the square is the centre point of a line drawn between B and F (the most distant corners of the two initial squares). Same is also true of a square made with A and G at opposite corners.

I'd be surprised if this was a new discovery, the Greeks were mad for this kind of shit, but I add it to the list of interesting mathsy things I've discovered to infuriate my mathematician friends who've never had an original thought in their lives ;)

Comments

[wildeabandon]

Your labelling is a bit confusing, especially as D can't be both the point furthest from B and the common corner. If you replace that D with F and call the first square ABCD then it makes a bit more sense, and sketches make it look plausible. I've got quite a bit of work to do before a meeting this afternoon, but I'll have a go at proving it afterwards. It does look like the sort of thing Euclid would have done.

[anicca]

whoops, that line is between B and F, sorry, typo :o)