Methods of Geometry by James T Smith

Methods of Geometry by James Smith

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

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