Squares

Applications

Squares are so well-established as the shape of tiles that the Latin word tessera, for a small tile as used in mosaics, comes from an ancient Greek word for the number four, referring to the four corners of a square tile. Graph paper, preprinted with a square tiling, is widely used for data visualization using Cartesian coordinates. The pixels of bitmap images, as recorded by image scanners and digital cameras or displayed on electronic visual displays, conventionally lie at the intersections of a square grid, and are often considered as small squares, arranged in a square tiling. Standard techniques for image compression and video compression, including the JPEG format, are based on the subdivision of images into larger square blocks of pixels. The quadtree data structure used in data compression and computational geometry is based on the recursive subdivision of squares into smaller squares.