Some squared squares and rectangles

Simple perfect squared squares and 2 * 1 squared rectangles of order 26

In this note tables of all simple perfect squared squares and simple 2 × 1 perfect squared rectangles of order 26 are presented.

Simple Perfect Squared Squares and 2 × 1 Squared Rectangles of Orders 21 to 24

Rectangles as sums of squares

In this paper we examine generalisations of the following problem posed by Laczkovich: Given an n × m rectangle with n and m integers, it can be written as a disjoint union of squares; what is the smallest number of squares that can be used? He also asked the corresponding higher dimensional analogue. For the two dimensional case Kenyon proved a tight logarithmic bound but left open the higher ...

Matching Points with Rectangles and Squares

In this paper we deal with the following natural family of geometric matching problems. Given a class C of geometric objects and a point set P , a C-matching is a set M ⊆ C such that every C ∈ M contains exactly two elements of P . The matching is perfect if it covers every point, and strong if the objects do not intersect. We concentrate on matching points using axis-aligned squares and rectan...

Majorization Algorithms for Inspecting Circles, Ellipses, Squares, Rectangles, and Rhombi

In several disciplines as diverse as shape analysis, location theory, quality control, archaeology, and psychometrics, it can be of interest to fit a circle through a set of points. We use the result that it suffices to locate a center for which the variance of the distances from the center to a set of given points is minimal. In this paper, we propose a new algorithm based on iterative majoriz...