Abstract: A set of geometrically patterned rectangular tiles includes a plurality of tiles each having a different pattern of arcuate segments thereon. The tiles may be used to form various interlocking and overlying circular, semicircular, and sinusoidal patterns or designs for various purposes, such as architectural and other designs. The tiles are also suited for the play of various games, with the object of the games being to form one or more continuous paths of joined arcuate segments enclosing other areas of assembled or adjacent tiles placed during the play of the games. Tiles may be divided generally into two groups, with one group having at least two different curved segments thereon, each differentiated from the other and with a single player or team controlling any one variation of the different segments, and another group having one or more different segments thereon for use as border or peripheral pieces for the first group.