Geodesic
Lattice motions of the Euclidean plane
Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 245-259 Cet article a éte moissonné depuis la source Math-Net.Ru

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The idea of lattice motions of the plane is introduced; these motions arise quite naturally from the point of view of probability. A complete description of such motions is given, from which follows their close connection with quadratic extensions of the field of rational numbers. Bibliography: 7 titles. 
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V. M. Maksimov. Lattice motions of the Euclidean plane. Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 245-259. http://geodesic.mathdoc.fr/item/SM_1980_37_2_a5/

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[6] V. M. Maksimov, “Ravnomernoe raspredelenie tochek i lokalnaya teorema dlya sluchainykh dvizhenii”, DAN SSSR, 232:2 (1977), 284–287 | MR | Zbl

[7] D. A. Kazhdan, “Ravnomernoe raspredelenie na ploskosti”, Trudy Mosk. matem. ob-va, 14 (1965), 299–305 | Zbl