Surveyor's formula, that's what it's called! Someone said something about a shoestring...
I just cited Vandermonde directly. The nice proof, IIRC, is you substitute in indeterminates x_1,...,x_n and note that if any two of them are equal, the whole thing is zero, then compute degrees? Only, then you still have to resolve the sign ambiguity, but I suppose that's done by example?
As for B3, I had no idea Fn was ⌊φn⌋. And yeah, I did get stuff with 3±√5. So probably I just miscalculated somewhere. Not sure how I would have proved it in that time, though, had I gotten it right.
no subject
Date: 2007-12-04 01:44 am (UTC)I just cited Vandermonde directly. The nice proof, IIRC, is you substitute in indeterminates x_1,...,x_n and note that if any two of them are equal, the whole thing is zero, then compute degrees? Only, then you still have to resolve the sign ambiguity, but I suppose that's done by example?
As for B3, I had no idea Fn was ⌊φn⌋. And yeah, I did get stuff with 3±√5. So probably I just miscalculated somewhere. Not sure how I would have proved it in that time, though, had I gotten it right.