Cuttings, partitions, coverings and tilings
Overview
Important
Cuttings, partitions, coverings, and tilings are fundamental concepts in combinatorial geometry. A cutting divides a figure into smaller pieces, a partition splits it into non-overlapping parts, a covering uses (possibly overlapping) shapes to cover a figure, and a tiling (or tessellation) fills a region with non-overlapping shapes without gaps.
Important properties
-
A partition divides a figure into non-overlapping parts that together make up the whole.
-
A covering may use overlapping shapes to ensure every point of the figure is included.
-
A tiling is a special kind of covering with no overlaps or gaps.
-
Cuttings can be done in many ways, such as by straight lines or curves, and may have special requirements (e.g., equal area, congruent pieces).