# Methods of Geometry by James Smith

Methods of Geometry by James T Smith

## Contents of Methods of Geometry

• Introduction
• Episodes
• This book
• 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