An irreducible rectangle tiling contains a spiral (Q1021307)

This paper deals with tiling of the square in the Euclidean plane by a finite system of rectangle tiles. Mutual congruency of tiles is not assumed. A tiling is called irreducible if for any two tiles the union of them is not a rectangle. A tiling is called generic if no four tiles meet in a point. A tiling containing only one tile is called trivial. A tile \(r\) in the interior of a square is called spiral if it is contained in a generic tiling of a square and for each edge \(e\) of \(r\) there exists a tile \(s\) adjacent to \(r\) such that the straight line containing \(e\) intersects the interior of \(s\). Studying properties of a tiling of rectangles the main result is reached. The main result is that a nontrivial generic irreducible tiling of a square contains a spiral.