ABSTRACT
This chapter begins with an exploration of paintings that depict objects with elliptic and hyperbolic surfaces. Euclid’s five postulates establish the assumptions at the basis of Euclidean geometry. The fifth postulate was questioned by mathematicians, who discovered two new geometries just as valid as Euclidean geometry: elliptic geometry and hyperbolic geometry. The existence of non-Euclidean geometries forced mathematicians to discriminate between absolute truth, which is unavailable in mathematics, and the equal validity of different mathematical theories. Non-Euclidean geometry has inspired artists to be less rigid and express more freedom in their work. The chapter concludes with a list of exercises.
