Euclidean and non-Euclidean geometries

Lecture 1 April 6 2013 Euclidean and Non-Euclidean geometries The earliest written text on geometry is an Egyptian papyrus dated to the 2 millennia B.C. The geometry at that time was a collection of empirically derived principles and formulas devised for application in construction, astronomy and surveying. The latter is where geometry got its name (Greek: geo"earth", -metron "measurement"). The geometry we know today, also known as Euclidean geometry is derived from the axiomatic formulation put forward by Euclid around 300 B.C. In this formulation Euclid put forward five postulates, which if assumed true, give rise to all the geometry we learned through middle and high-school. The postulates may seem very natural and at times even trivial, yet they cannot be derived logically from any reduced set of assumptions. The postulates read: