A lowest order simple perfect 2 × 1 squared rectangle

Simple perfect squared square of lowest order

This note is to report the existence of a simple perfect dissection of a square into 21 unequal squares.

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

Simple perfect square-cylinders of low order

We report the existence of two simple perfect square-cylinders of order 20 shown in Figs. 1 and 2. Dissected cylinders are associated with graphs which we call cyl-nets. A cyl-net is obtained from a dissected cylinder in the following way. The two rims of the cylinder are associated with two vertices which are called “source” and “sink,” respectively. Each horizontal line is associated with a v...

Hardness in Perfect Rectangle Packing Problems

Rectangle Packing is considered a difficult NP-problem which has several application areas such as integrated circuit systems, and pallet packing. Generally, Rectangle Packing Problems consist of a set of rectangles for which a configuration must be found, the intention is to minimise the surface-area of the configurations bounding box. Existing research has predominantly investigated algorithm...