Geodesic
Covering of a rectangle with squares from both sides
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 16-26

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper provides an elementary proof of Kenyon's theorem that periodic tiling of a plane by squares with periods $(1,0)$ and $(0,\lambda)$ is possible only if $\lambda=p\pm\sqrt{q^2 - r^2}$ for some rational $p\geq q\geq r\geq 0$. A similar new result is proved about covering of a rectangle with squares from both sides in one layer. The paper also proves a necessary and sufficient condition for covering with equal squares. 
@article{DVMG_2023_23_1_a2,
     author = {M. D. Dmitriev and F. Yu. Ozhegov},
     title = {Covering of a rectangle with squares from both sides},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {16--26},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a2/}
}
TY  - JOUR
AU  - M. D. Dmitriev
AU  - F. Yu. Ozhegov
TI  - Covering of a rectangle with squares from both sides
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2023
SP  - 16
EP  - 26
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a2/
LA  - ru
ID  - DVMG_2023_23_1_a2
ER  - 
%0 Journal Article
%A M. D. Dmitriev
%A F. Yu. Ozhegov
%T Covering of a rectangle with squares from both sides
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2023
%P 16-26
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a2/
%G ru
%F DVMG_2023_23_1_a2
M. D. Dmitriev; F. Yu. Ozhegov. Covering of a rectangle with squares from both sides. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 16-26. http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a2/