A proportion in which a straight line or rectangle is divided into two unequal parts in such a way that the ratio of the smaller to the greater part is the same as that of the greater to the whole. Like the mathematical value pi, it cannot be expressed as a finite number, but an approximation is 8 : 13 or 0.618 : 1. The proportion has been known since antiquity and has been said to possess inherent aesthetic value because of an alleged correspondence with the laws of nature or the universe. It was much studied during the Renaissance, and Luca Pacioli, the most famous mathematician of his day and a friend of Leonardo and of Piero della Francesca, wrote a book on it called Divina proportione (1509). In accordance with the tendencies of the time, Pacioli's book, illustrated with drawings by Leonardo, credits this ‘divine proportion’ with various mystical properties and exceptional beauties both in science and in art.