Geodesic
Cutting Polygons Composed of Equal Rectangles into Similar Rectangles
Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 736-743

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Assume that a polygon is composed of equal rectangles. We find all quadratic irrationalities $r$ for which the polygon under study can be cut into similar rectangles with aspect ratio $r$.
Keywords: cutting, tiling, additive function, rectangle, quadratic irrationality. 
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     author = {I. V. Novikov},
     title = {Cutting {Polygons} {Composed} of {Equal} {Rectangles} into {Similar} {Rectangles}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {736--743},
     publisher = {mathdoc},
     volume = {110},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a7/}
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I. V. Novikov. Cutting Polygons Composed of Equal Rectangles into Similar Rectangles. Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 736-743. http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a7/