Chapter1 Ancient Artand Geometry

• exposé

Chapter 1 Ancient Art and Geometry Math 4520 Spring 2010 1.1 Introduction In Plato's view, only that which turned the soul's eye from the material world to objects of pure thought was worthy of a philosopher's study. Music, astronomy, arithmetic, and espe- cially geometry were particularly recognized. The idea was to start with certain unquestioned assumptions and precise definitions and proceed logically and rigorously from there. Euclid of Alexandria, a student of the Platonic school, lived from 323 BC to 283 BC.

• axioms into classes of incidence
• liberal interpretation of the axioms
• parent of a worthless progeny
• existence of a consistent system with an alternative axiom
• intersection with the sphere of a plane
• hyperbolic plane
• model
• many people
• system