A Family of Fibonacci Lattices. II

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概要

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• We give a rigorous proof that the cyclic self-similar deflationary structure of thetype discussed in the previous paper underlies a certain wider class of shifted Fibo-nacci sequences. The proof is equivalent to showing that an itvitial phase of the type0.=r.-I-r./r (r=golden mean, r, r.=rational numbers) is expanded into a recurringalternating power series of 1 / r (including finite alternating otter. Recurring decimalseries expansion in powers of other irrational numbers is also mentioned. For cornpleteness, we also show that a pair of "least units of cycle" is automatically generatedon deflation in the case of Fibonacci sequences that extend in both directions.[Fibonacci sequence, local isomorphism, self-similarity, cycle, phason, recurring lf decimal, irrational number{

• 1990-11-15

著者

• GODA Masaki

  Faculty of Engineering, Niigata University

• OGAWA Tohru

  Institute of Applied Physics, University of Tsukuba

• TAKEMORI Tadashi

  Institute of Materials Science, University of Tsukuba

• Goda Masaki

  Faculty Of Engeneering Niigata University

• Goda Masaki

  Faculty Of Engineering Niigata University:

• Ogawa Tohru

  Institute Of Applied Physics University Of Tsukuba

• KUBO Haruhiko

  Graduate School of Science and Technology,Niigata University

• Kubo Haruhiko

  Graduate School Of Science And Technology Niigata University

• Takemori Tadashi

  Institute Of Applied Physics University Of Tsukuba

• OGAWA Tohru

  Institute of Applied Physics,University of Tsukuba

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