Architects use mathematics for several reasons, leaving aside the necessary use of mathematics in the engineering of buildings. Firstly, they use geometry because it defines the spatial form of a building. Secondly, they use mathematics to design forms that are considered beautiful or harmonious. From the time of the Pythagoreans with their religious philosophy of number, architects in ancient Greece, ancient Rome, the Islamic world and the Italian Renaissance have chosen the proportions of the built environment – buildings and their designed surroundings – according to mathematical as well as aesthetic and sometimes religious principles. Thirdly, they may use mathematical objects such as tessellations to decorate buildings. Fourthly, they may use mathematics in the form of computer modelling to meet environmental goals, such as to minimise whirling air currents at the base of tall buildings.