In this paper we prove two results about tilings of orthogonal polygons. (1) Let P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. Anâ€¦ (More)

Let C be a plane convex body. The relative distance (or C-distance) of points a, b âˆˆ R2 is defined by the ratio of the Euclidean length of the line-segment ab to half of the Euclidean length of aâ€¦ (More)

We need some definitions from [1]. Let C âŠ‚ R2 be a convex body. A chord pq of C is called an affine diameter of C, if there is no longer parallel chord in C. The ratio of |ab| to 1 2 |aâ€²bâ€²|, whereâ€¦ (More)

Let C be a plane convex body. For arbitrary points , denote by , n a b E ïƒŽ ab the Euclidean length of the line-segment . Let be a longest chord of C parallel to the line-segment . The relativeâ€¦ (More)