منابع مشابه
T he square Fibonacci tiling *
We introduce the 2-dimensional square Fibonacci tiling and its generalization to higher dimensions as models for quasicrystals without ‘forbidden’ symmetries. We derive some of the basic mathematical properties of the tiling as well as calculate its diffraction pattern. We discuss the relevance of the Fibonacci tiling for quasicrystal research and for applications in other fields. 2002 Elsevi...
متن کاملElectronic Energy Spectra and Wave Functions on the Square Fibonacci Tiling
We study the electronic energy spectra and wave functions on the square Fibonacci tiling, using an off-diagonal tight-binding model, in order to determine the exact nature of the transitions between different spectral behaviors, as well as the scaling of the total bandwidth as it becomes finite. The macroscopic degeneracy of certain energy values in the spectrum is invoked as a possible mechani...
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We describe a tiling of the plane, motivated by architectural constructions of domes, in which the Fibonacci series appears in many ways.
متن کاملTiling Proofs of Some Fibonacci-lucas Relations
We provide tiling proofs for some relations between Fibonacci and Lucas numbers, as requested by Benjamin and Quinn in their text, Proofs that Really Count. Extending our arguments yields Gibonacci generalizations of these identities.
متن کاملTiling a Square with Eight Congruent Polyominoes
The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangular order 8, and asks if it can be generalized to a family of rectifiable polyominoes. Here we show...
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ژورنال
عنوان ژورنال: Journal of Alloys and Compounds
سال: 2002
ISSN: 0925-8388
DOI: 10.1016/s0925-8388(02)00169-x