Geometry, Fall 2016

     Main source for exercises and theory is following book:

Richard S. Millman and George D. Parker: "Geometry A Metric Approach with Models" (Undergraduate Texts in Mathematics), Springer, 1990.

Also very interesting book is by George E. Martin: "The Foundations of Geometry and the Non-Euclidean Plane" (Undergraduate Texts in Mathematics), Springer-Verlag, New York (1982)

Incidence and Metric Geometry
Weeks 1--3
• Definition and Models of Incidence Geometry    • Metric geometry    • Special Coordinate Systems				problems problems problems
Betweenness and Elementary Figures
Weeks 4, 5
• An Alternative Description of the Cartesian Plane    • Betweenness    • Line segments and Rays    • Angles and Triangles				problems problems
Plane Separation
Weeks 6--8
• The Plane Separation Axiom    • PSA for the Euclidean and Poincare Planes    • Pasch Geometries    • Interiors and the Crossbar Theorem    • Convex Quadrilaterals				problems problems problems
Angle Measure
Weeks 8, 9
• The Measure of an Angle    • Perpendicularity and Angle Congruence    • Euclidean and Poincare Angle Measure				problems problems
Neutral Geometry
Weeks 10--12
• The Side-Angle-Side Axiom    • Basic Triangle Congruence Theorems    • The Exterior Angle Theorem and Its Consequences    • Right Triangles    • Circles and Their Tangent Lines    • The Two Circle Theorem				problems problems problems
The Theory of Parallels
Weeks 13, 14
• The Existence of Parallel Lines    • Saccheri Quadrilaterals    • The Critical Function				problems problems
Hyperbolic Geometry
Weeks 14, 15
• Asymptotic Rays and Triangles    • Angle Sum and the Defect of a Triangle    • The Distance Between Parallel Lines				problems problems

Links that follow below, I have found very useful:


On Slovenian:

   • Geometrija; I. Kovacs and K. Kutnar

   • Afina in projektivna geometrija; A. Vavpetič


On English:

   • http://www.maths.uq.edu.au/~ejb/math3301/2008/home.html

   • http://math.furman.edu/~dcs/courses/math36/assignments.html