Fibonacci 字型與Fibonacci 字性質已有很多有趣的結果。本篇論文將討論無窮Fibonacci 字之有趣性質。

For all x E R,define L^J = « where n E Z, n < x < n + 1. For all x G R, define x] = n. where
n E Z, n — 1 < Jt < n. Let a =丄~ . Define the following two-way infinite binary words.
(a) G = d.nd.n+1---d.1d0d1-*-dndn+1---, where the nth letter dn = [(n + l)c?J — [na,rt G Z.
(b) H = e.ne.n+i-" - e.i e0ei …enSn+i.…，where the nth letter en =『(n + 1)®1 — fnsl, n E Z.
Hence G and H are called two-way infinite words. In this paper, we will find all square prefixes of Gm (or Hm) for each m 6 Z.