Tessellations

Almost everyone has at one time or another been intrigued by mosaic patterns. Figure 11.31 illustrates seventeen tilings of the plane. A tiling of the plane is also called a mosaic, tessellation, or paving of the plane. Tiling as an art predates human history and, perhaps, reached its zenith in the Moorish forts, palaces, and mosques near the end of what Westerners call the Middle Ages. Except for an initial study by the astronomer Johannes Kepler (1571–1630), little formal mathematical investigation of tilings took place before the end of the last century. Much of what has been done is the work of chemists and crystallographers. Today, mathematicians are taking more interest in this ancient topic.