64 = 65.
Hint. The explanation involves the famous Fibonacci numbers.
In general, if Fk denotes the k-th Fibonacci number, a Fn×Fn square can be rearranged into a Fn-1×Fn+1 rectangle according to Cassini’s identity that is easily proven by induction
| (2) | Fn+1·Fn+1 – FnFn+2 = (-1)n |
There, that explains it, now move along.
Oh this is driving me crazy! There’s just no way I can compute this. Your explanation is fantastic but so far over my head I can see con-trails.
@David: “contrails…” HAR. Love your company name. Dorey Media. (Doe Ray – door ray? – Meeee dia) Clevah.