Geometrical aspects of the algebraic number related to quasicrystals
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Abstract
A quasicrystal is a mathematical term for an infinite point or tiling space. It possesses several intersecting features, including Delone, relative discreteness, and self-similarities. The model set is the basic form in which the physical quasicrystals are represented. Pisot numbers are used to identify the one-dimensional model sets' adjacent points. The quadratic irrational numbers are related to all one-dimensional model sets that have been experimentally discovered the paper offers mathematical models of quasicrystals with particular attention given to cut and projection sets for the eight folded symmetry and discuss about one dimensional cut and projection set.
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