Methods of Geometry by James T Smith
Contents of Methods of Geometry
- Introduction
- Episodes
- Advanced geometry
- This book
- Reading about geometry
- Projects
- Foundations
- Geometry as applied mathematics
- Need for rigor
- Axiomatic method
- Euclid’s Elements
- Coordinate geometry
- Foundation problem
- Parallel axiom
- Firm foundations
- Geometry as pure mathematics
- Exercises and projects
- Elementary Euclidean geometry
- Incidence geometry
- Ruler axiom and its consequences
- Pasch’s axiom and the separation theorems
- Angles and the protractor axioms
- Congruence
- Perpendicularity
- Parallel axiom and related theorems
- Area and Pythagoras’ theorem
- Similarity
- Polyhedral volume
- Coordinate geometry
- Circles and spheres
- Arcs and trigonometric functions
- Exercises on elementary geometry
- Exercises on the incidence and ruler axioms
- Exercises related to Pasch’s axiom
- Exercises on congruence and perpendicularity
- Exercises involving the parallel axiom
- Exercises on similarity and Pythagoras’ theorem
- Exercises on circles and spheres, part
- Exercises on area
- Exercises on volume
- Exercises on circles and spheres, part
- Exercises on coordinate geometry
- Some triangle and circle geometry
- Four concurrence theorems
- Menelaus’ theorem
- Desargues’ theorem
- Ceva’s theorem
- Trigonometry
- Vector products
- Centroid
- Orthocenter
- Incenter and excenters
- Euler line and Feuerbach circle
- Exercises
- Plane isometrles and similarities
- Transformations
- Isometries
- Reflections
- Translations
- Rotations
- Structure theorem
- Glide reflections
- Isometries and orthogonal matrices
- Classifying isometries
- Similarities
- Exercises
- Three dimensional isometries and similarities
- Isometries
- Reflections
- Translations and rotations
- Glide and rotary reflections
- Classifying isometries
- Similarities
- Exercises
- Symmetry
- Polygonal symmetry
- Friezes
- Wallpaper ornaments
- Polyhedra
- Exercises
