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| Preface | |
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| Author | |
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| Lines, Distance, Segments, and Rays | |
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| Intended Goals | |
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| Axioms of Alignment | |
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| A Glimpse at Finite Geometry | |
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| Metric Geometry | |
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| Eves' 25-Point Affine Geometry: A Model for Axioms 0-4 | |
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| Distance and Alignment | |
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| Properties of Betweenness: Segments and Rays | |
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| Coordinates for Rays | |
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| Geometry and the Continuum | |
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| Segment Construction Theorems | |
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| Angles, Angle Measure, and Plane Separation | |
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| Angles and Angle Measure | |
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| Plane Separation | |
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| Consequences of Plane Separation: The Postulate of Pasch | |
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| The Interior of an Angle: The Angle Addition Postulate | |
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| Angle Construction Theorems | |
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| Consequences of a Finite Metric | |
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| Unified Geometry: Triangles and Congruence | |
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| Congruent Triangles: SAS Hypothesis | |
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| A Metric for City Centers | |
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| The SAS Postulate and the ASA and SSS Theorems | |
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| Euclid's Superposition Proof: An Alternative to Axiom 12 | |
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| Locus, Perpendicular Bisectors, and Symmetry | |
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| The Exterior Angle Inequality | |
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| Inequalities for Triangles | |
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| Further Congruence Criteria | |
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| Special Segments Associated with Triangles | |
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| Quadrilaterals, Polygons, and Circles | |
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| Quadrilaterals | |
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| Congruence Theorems for Convex Quadrilaterals | |
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| The Quadrilaterals of Saccheri and Lambert | |
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| Polygons | |
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| Circles in Unified Geometry | |
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| Three Geometries | |
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| Parallelism in Unified Geometry and the Influence of � | |
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| Elliptic Geometry: Angle-Sum Theorem | |
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| Pole-Polar Theory for Elliptic Geometry | |
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| Angle Measure and Distance Related: Archimedes' Method | |
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| Hyperbolic Geometry: Angle-Sum Theorem | |
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| A Concept for Area: AAA Congruence | |
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| Parallelism in Hyperbolic Geometry | |
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| Asymptotic Triangles in Hyperbolic Geometry | |
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| Euclidean Geometry: Angle-Sum Theorem | |
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| Median of a Trapezoid in Euclidean Geometry | |
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| Similar Triangles in Euclidean Geometry | |
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| Pythagorean Theorem | |
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| Inequalities for Quadrilaterals: Unified Trigonometry | |
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| An Inequality Concept for Unified Geometry | |
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| Ratio Inequalities for Trapezoids | |
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| Ratio Inequalities for Right Triangles | |
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| Orthogonal Projection and �Similar� Triangles | |
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| Unified Trigonometry: The Functions c(�) and s(�) | |
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| Trigonometric identities | |
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| Classical Forms for c(�) and s(�) | |
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| Lambert Quadrilaterals and the Function C(u) | |
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| Identities for C(u) | |
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| Classical Forms for C(u) | |
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| The Pythagorean Relation for Unified Geometry | |
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| Classical Unified Trigonometry | |
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| Beyond Euclid: Modern Geometry | |
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| Directed Distance: Stewart's Theorem and the Cevian Formula | |
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| Formulas for Special Cevians | |
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| Circles: Power Theorems and Inscribed Angles | |
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| Using Circles in Geometry | |
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| Cross Ratio and Harmonic Conjugates | |
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| The Theorems of Ceva and Menelaus | |
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| Families of Mutually Orthogonal Circles | |
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| Transformations in Modern Geometry | |
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| Projective Transformations | |
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| Affine Transformations | |
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| Similitudes and Isometries | |
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| Line Reflections: Building Blocks for Isometries and Similitudes | |
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| Translations and Rotations | |
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| Circular Inversion | |
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| Non-Euclidean Geometry: Analytical Approach | |
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| Law of Sines and Cosines for Unified Geometry | |
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| Unifying Identities for Unified Trigonometry | |
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| Half-Angle Identities for Unified Geometry | |
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| The Shape of a Triangle in Unified Geometry: Cosine Inequality | |
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| The Equations of Gauss: Area of a Triangle | |
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| Directed Distance: Theorems of Menelaus and Ceva | |
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| Poincar�'s Model for Hyperbolic Geometry | |
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| Other Models: Surface Theory | |
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| Hyperbolic Parallelism and Bolyai's Ideal Points | |
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| Sketchpad Experiments | |
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| Intuitive Spherical Geometry | |
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| Proof in Geometry | |
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| The Real Numbers and Least Upper Bound | |
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| Floating Triangles/Quadrilaterals | |
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| Axiom Systems for Geometry | |
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| Solutions to Selected Problems | |
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| Bibliography | |
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| Index | |