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Chebyshevskii Sb., 2015, Volume 16, Issue 2, Pages 273–281 (Mi cheb402)  

On rational directions in the flat lattice

M. I. Shtogrin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Rational and irrational rotations for the set of rational directions in the flat point lattice are considered. It is proved that in the case of rational rotations an order of noncrystallographic turn can be only 8 or 12. The set of rational directions in the rectangular point lattice with metric quadratic form $x^2+\lambda^2y^2$ and arbitrary its centering has irrational rotation if and only if the number $\lambda^2$ is rational.
Bibliography: 3 titles.

Keywords: lattice, unit cell, rational direction, rotation, angle, tangent.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


Full text: PDF file (244 kB)
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UDC: 514.11+514.87
Received: 08.05.2015

Citation: M. I. Shtogrin, “On rational directions in the flat lattice”, Chebyshevskii Sb., 16:2 (2015), 273–281

Citation in format AMSBIB
\Bibitem{Sht15}
\by M.~I.~Shtogrin
\paper On rational directions in the flat lattice
\jour Chebyshevskii Sb.
\yr 2015
\vol 16
\issue 2
\pages 273--281
\mathnet{http://mi.mathnet.ru/cheb402}
\elib{http://elibrary.ru/item.asp?id=23614022}


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