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15
ASCHER’S DRAWING
If a plane is covered with a polygon so that two polygons have either a common side, a common vertex, or have no common points at all, then such a covering is called parquet.
In our magazine (see «Kvant» No. 3, 1970, p. 21) we presented a number of problems related to parquet floors.
For some parquets, it is possible to specify plane transformations that transform the figures that make up the parquet into each other so that the parquet itself does not change.
For the parquet shown on this figure, its transformations also do not change: rotation around the point by 60° and symmetry with respect to straight line l. What other transformations can you point out that do not change this parquet?
You see a completely different kind of parquet on figure by the Dutch artist Escher (see cover). This parquet is replaced by the fact that one of the transformations that does not change it is doubling all distances relative to the center (similarity transformation). Therefore, strictly speaking, figure depicts an infinite number of shrinking lizards. Try to come up with other parquets that do not change their similarity during transformations.
L. Limanov