6 citations · 11 across the 16 of their papers we have counts for
6 papers · 1 filter
Invariants and equidecomposability in rings of polygons with sides of given directions
Gergely Kiss, Miklós Laczkovich
We investigate equidecomposability in the ring of polygons with sides restricted to given directions and using only translations. Extending classical results of Dehn and Hadwiger,…
Quadrilateral reptiles
Miklos Laczkovich
A polygon is called a reptile, if it can be decomposed into nonoverlapping and congruent polygons similar to . We prove that if a cyclic quadrilateral is a reptile,…
Irregular tilings of regular polygons with similar triangles
M. Laczkovich
We say that a triangle tiles a polygon , if can be dissected into finitely many nonoverlapping triangles similar to . We show that if , then there are at most t…
The Kakeya problem for circular arcs
Kornélia Héra, Miklós Laczkovich
We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.
Closed sets with the Kakeya property
Marianna Csörnyei, Kornélia Héra, Miklós Laczkovich
We say that a planar set has the Kakeya property if there exist two different positions of such that can be continuously moved from the first position to the second wit…
Magic mirrors, dense diameters, Baire category
Imre Bárány, Miklós Laczkovich
An old result of Zamfirescu says that for most convex curves in the plane most points in lie on infinitely many normals to , where most is meant in Baire category sens…