CreateSpace, 2015. — 190 p.The Author: Anton Petrunin (Russia), professor at Penn. State UniversityThe book is meant to be rigorous, conservative, elementary and minimalistic. At the same time it includes about the maximum what students can absorb in one semester. Approximately third of the material used to be covered in high school, not any more. The present book is based on the courses given by the author at the Penn State as an introduction into Foundations of Geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular they are familiar with the real numbers and continuity. It makes possible to cover the material faster and in a more rigorous way than it could be done in high school.Introduction.
Preliminaries.
Euclidean geometry.
The Axioms.
Half-planes.
Congruent triangles.
Perpendicular lines.
Parallel lines and similar triangles
Triangle geometry
Inversive geometry.
Inscribed angles
Inversion
Non-Euclidean geometry.
Absolute plane
Hyperbolic plane
Geometry of h-plane
Incidence geometry.
Affine geometry
Projective geometry
Additional topics.
Spherical geometry
Projective model
Complex coordinates
Geometric constructions
Area
References.
Hints
Index
Used resources
