Fundamentals of Geometry Oleg A. Belyaev [email protected] February 28, 2007 Geometry Points, Lines & Planes Collinear points are points that lie on the same line. Chapter 1 Basic Geometry An intersection of geometric shapes is the set of points they share in common. Hyperbolic Geometry can all be derived from Projective Geometry by adding a suitable metric to (a subset of) it. l and m intersect at point E. l and n intersect at point D. m and n intersect in line m 6 , , , n , &. Purpose of this note is to provide an introduction to some aspects of hyperbolic geometry. So, if we want to investigate the fundamentals of Geometry, it is only natural to do this rstly and mainly on Projective Geometry. Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. 1.6 Axiom systems In that sense Projective Ge-ometry is more fundamental than the other geometries. Hyperbolic Geometry by Charles Walkden. The choice of the axioms and the investigation of their relations to one another is a problem which, since the time of Euclid, has been discussed in numerous These fundamental principles are called the axioms of geometry.