93.43 Fibonacci relationships geometrically

摘要

The object of this note is to generate geometrically the Fibonaccisequence and then use the construction to illustrate relationships (all ofwhich can be found in [1]) involving the sequence. The Fibonacci sequenceF_nis defined recursively as F_0= 0, F_1=1, andF_n =F_(n-1) +F_(n-2)for allnatural numbers n > 1. Substituting the form F_(n-10= F_(n+1) — F_ninto thewell-known relationship F_(n-1)F_(n+10— (F_n)~2= (