Pascal Triange - Fibonacci Sequence

[l-1j-cho]

Does anyone have a DIRECT proof of the relationship between Pascal Triangle and Fibonacci Sequence? I mean not like induction or other method of proof but a direct method. I try to google it but couldn't find one

 

[DrBloke]

One property of the triangle is revealed if the rows are left-justified. In the triangle below, the diagonal coloured bands sum to successive Fibonacci numbers.

http://en.wikipedia.org/wiki/Pascal_triangle#Overall_patterns_and_properties"

but that doesn't really answer your question rather than just state it. I think http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html#whypascal" does though.