Classical Geometry Euclidean, Transformational, Inversive, and Projective.

Detalles Bibliográficos
Autor principal: Leonard, I. E.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Half Title page
  • Title page
  • Copyright page
  • Preface
  • Part I: Euclidean Geometry
  • Chapter 1: Congruency
  • 1.1 Introduction
  • 1.2 Congruent Figures
  • 1.3 Parallel Lines
  • 1.4 More About Congruency
  • 1.5 Perpendiculars and Angle Bisectors
  • 1.6 Construction Problems
  • 1.7 Solutions to Selected Exercises
  • 1.8 Problems
  • Chapter 2: Concurrency
  • 2.1 Perpendicular Bisectors
  • 2.2 Angle Bisectors
  • 2.3 Altitudes
  • 2.4 Medians
  • 2.5 Construction Problems
  • 2.6 Solutions to the Exercises
  • 2.7 Problems
  • Chapter 3: Similarity
  • 3.1 Similar Triangles
  • 3.2 Parallel Lines and Similarity
  • 3.3 Other Conditions Implying Similarity
  • 3.4 Examples
  • 3.5 Construction Problems
  • 3.6 The Power of a Point
  • 3.7 Solutions to the Exercises
  • 3.8 Problems
  • Chapter 4: Theorems of Ceva and Menelaus
  • 4.1 Directed Distances, Directed Ratios
  • 4.2 The Theorems
  • 4.3 Applications of Ceva's Theorem
  • 4.4 Applications of Menelaus' Theorem
  • 4.5 Proofs of the Theorems
  • 4.6 Extended Versions of the Theorems
  • 4.7 Problems
  • Chapter 5: Area
  • 5.1 Basic Properties
  • 5.2 Applications of the Basic Properties
  • 5.3 Other Formulae for the Area of a Triangle
  • 5.4 Solutions to the Exercises
  • 5.5 Problems
  • Chapter 6: Miscellaneous Topics
  • 6.1 The Three Problems of Antiquity
  • 6.2 Constructing Segments of Specific Lengths
  • 6.3 Construction of Regular Polygons
  • 6.4 Miquel's Theorem
  • 6.5 Morley's Theorem
  • 6.6 The Nine-Point Circle
  • 6.7 The Steiner-Lehmus Theorem
  • 6.8 The Circle of Apollonius
  • 6.9 Solutions to the Exercises
  • 6.10 Problems
  • Part II: Transformational Geometry
  • Chapter 7: The Euclidean Transformations or Isometries
  • 7.1 Rotations, Reflections, and Translations
  • 7.2 Mappings and Transformations
  • 7.3 Using Rotations, Reflections, and Translations
  • 7.4 Problems
  • Chapter 8: The Algebra of Isometries
  • 8.1 Basic Algebraic Properties
  • 8.2 Groups of Isometries
  • 8.3 The Product of Reflections
  • 8.4 Problems
  • Chapter 9: The Product of Direct Isometries
  • 9.1 Angles
  • 9.2 Fixed Points
  • 9.3 The Product of Two Translations
  • 9.4 The Product of a Translation and a Rotation
  • 9.5 The Product of Two Rotations
  • 9.6 Problems
  • Chapter 10: Symmetry and Groups
  • 10.1 More About Groups
  • 10.2 Leonardo's Theorem
  • 10.3 Problems
  • Chapter 11: Homotheties
  • 11.1 The Pantograph
  • 11.2 Some Basic Properties
  • 11.3 Construction Problems
  • 11.4 Using Homotheties in Proofs
  • 11.5 Dilatation
  • 11.6 Problems
  • Chapter 12: Tessellations
  • 12.1 Tilings
  • 12.2 Monohedral Tilings
  • 12.3 Tiling with Regular Polygons
  • 12.4 Platonic and Archimedean Tilings
  • 12.5 Problems
  • Part III: Inversive and Projective Geometries
  • Chapter 13: Introduction to Inversive Geometry
  • 13.1 Inversion in the Euclidean Plane
  • 13.2 The Effect of Inversion on Euclidean Properties
  • 13.3 Orthogonal Circles
  • 13.4 Compass-Only Constructions

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