Classical geometry Euclidean, transformational, inversive, and projective
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understa...
| Main Authors: | , , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2014
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| Subjects: | |
| Online Access: | |
| Collection: | O'Reilly - Collection details see MPG.ReNa |
Table of Contents:
- 6.7 The Steiner-Lehmus Theorem6.8 The Circle of Apollonius; 6.9 Solutions to the Exercises; 6.10 Problems; PART II TRANSFORMATIONAL GEOMETRY; 7 The Euclidean Transformations or lsometries; 7.1 Rotations, Reflections, and Translations; 7.2 Mappings and Transformations; 7.2.1 Isometries; 7.3 Using Rotations, Reflections, and Translations; 7.4 Problems; 8 The Algebra of lsometries; 8.1 Basic Algebraic Properties; 8.2 Groups of Isometries; 8.2.1 Direct and Opposite Isometries; 8.3 The Product of Reflections; 8.4 Problems; 9 The Product of Direct lsometries; 9.1 Angles; 9.2 Fixed Points
- 4.7 Problems5 Area; 5.1 Basic Properties; 5.1.1 Areas of Polygons; 5.1.2 Finding the Area of Polygons; 5.1.3 Areas of Other Shapes; 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; 6 Miscellaneous Topics; 6.1 The Three Problems of Antiquity; 6.2 Constructing Segments of Specific Lengths; 6.3 Construction of Regular Polygons; 6.3.1 Construction of the Regular Pentagon; 6.3.2 Construction of Other Regular Polygons; 6.4 Miquel's Theorem; 6.5 Morley's Theorem; 6.6 The Nine-Point Circle; 6.6.1 Special Cases
- Includes bibliographical references and index
- 2.6 Solutions to the Exercises2.7 Problems; 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; 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; 4.6.1 Ceva's Theorem in the Extended Plane; 4.6.2 Menelaus' Theorem in the Extended Plane
- 9.3 The Product of Two Translations9.4 The Product of a Translation and a Rotation; 9.5 The Product of Two Rotations; 9.6 Problems; 10 Symmetry and Groups; 10.1 More About Groups; 10.1.1 Cyclic and Dihedral Groups; 10.2 Leonardo's Theorem; 10.3 Problems; 11 Homotheties; 11.1 The Pantograph; 11.2 Some Basic Properties; 11.2.1 Circles; 11.3 Construction Problems; 11.4 Using Homotheties in Proofs; 11.5 Dilatation; 11.6 Problems; 12 Tessellations; 12.1 Tilings; 12.2 Monohedral Tilings; 12.3 Tiling with Regular Polygons; 12.4 Platonic and Archimedean Tilings; 12.5 Problems
- CLASSICAL GEOMETRY: Euclidean, Transformational, Inversive, and Projective; Copyright; CONTENTS; Preface; PART I EUCLIDEAN GEOMETRY; 1 PART I EUCLIDEAN GEOMETRY Congruency; 1.1 Introduction; 1.2 Congruent Figures; 1.3 Parallel Lines; 1.3.1 Angles in a Triangle; 1.3.2 Thales' Theorem; 1.3.3 Quadrilaterals; 1.4 More About Congruency; 1.5 Perpendiculars and Angle Bisectors; 1.6 Construction Problems; 1.6.1 The Method of Loci; 1.7 Solutions to Selected Exercises; 1.8 Problems; 2 Concurrency; 2.1 Perpendicular Bisectors; 2.2 Angle Bisectors; 2.3 Altitudes; 2.4 Medians; 2.5 Construction Problems