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| A Panoramic View of Geometry | |
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| Introduction | |
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| Geometry in the Physical World | |
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| Geometry as a Mathematical System | |
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| Geometry as a Formal Axiomatic Structure | |
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| Aesthetic and Recreational Aspects of Geometry | |
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| Summary | |
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| Basic Ideas of Geometry | |
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| Introduction | |
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| Points, Lines, and Their Relationships | |
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| Basic Geometric Figures and Their Measures | |
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| Line and Angle Relationships | |
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| More about Triangles and Quadrilaterals | |
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| Discovering Polygon Relationships | |
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| Introduction | |
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| More About Polygons | |
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| Symmetry of Polygons | |
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| Construction of Regular Polygons | |
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| Star Polygons | |
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| Discovering Theorems About Polygons | |
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| Patterns of Polygons | |
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| Tessellations | |
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| Introduction | |
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| Tessellations of Polygons | |
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| Tessellations with Regular Polygons | |
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| Analysis of Semi-Regular Tessellations | |
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| Three-Mirror Kaleidoscope | |
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| Tessellations of Curved Patterns | |
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| Geometry in 3-Dimensions | |
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| Introduction | |
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| Regular Polyhedra | |
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| Symmetry in Space | |
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| Semi-Regular Polyhedra | |
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| Tessellations of Space | |
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| Measurement--Length, Area, and Volume | |
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| Introduction | |
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| Need for Standard Units in Measuring | |
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| Metric System of Measuring Units | |
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| Measuring Length | |
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| Measuring Area | |
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| Measuring Volume and Capacity | |
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| Measuring Mass and Weight | |
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| Motions in Geometry | |
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| Introduction | |
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| Slides or Translations | |
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| Turns or Rotations | |
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| Flips or Reflections | |
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| Combining Slides, Turns, and Flips | |
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| Motions and Congruence | |
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| Magnification and Similarity | |
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| Introduction | |
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| Magnification | |
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| Properties of Magnifications | |
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| Similarity | |
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| Topology | |
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| Introduction | |
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| Topological Equivalence | |
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| Networks | |
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| Jordan Curve Theorem | |
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| Contiguous Regions | |
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| Four Color Problem | |
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| Number Patterns in Geometry | |
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| Introduction | |
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| Patterns of Points | |
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| Patterns of Lines | |
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| Pattern and Proof | |
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| Pascal's Triangle and Related Patterns | |
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| Appendices | |
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| Using Logo in Geometry | |
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| Constructions | |
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| Metric Units | |
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| Critical Thinking | |
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| Computer Explorations in Geometry | |
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| Glossary, Postulates, and Theorems | |