Geometry
An Investigative Approach
2nd Edition
Published on 1. January 1992
Book
Hardback
480 pages
978-0-201-21795-7 (ISBN)
Description
This second edition effectively prepares education students, elementary or secondary school teachers, or college instructors to teach geometry. It can also serve as a useful reference for anyone in these fields. This book can also serve as a textbook in an elementary plane geometry course having an investigative emphasis. The text explores geometric concepts inductively first and then presents deductive proof. Students are encouraged to explore geometric ideas using constructions, laboratory materials, and various other investigative techniques. The text promotes student interaction by emphasizing small group investigation. This edition helps teachers implement the latest NCTM standards by addressing the development of critical thinking, the use of technology to explore geometric relationships, the use of geometry as a medium for problem solving, and the importance of applications in geometry.
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Content
1. A Panoramic View of Geometry.
Introduction, Geometry in the Physical World, Geometry as a Mathematical System, Geometry as a Formal Axiomatic Structure, Aesthetic and Recreational Aspects of Geometry, Summary.
2. Basic Ideas of Geometry.
Introduction, Points, Lines, and Their Relationships, Basic Geometric Figures and Their Measures, Line and Angle Relationships, More about Triangles and Quadrilaterals.
3. Discovering Polygon Relationships.
Introduction, More About Polygons, Symmetry of Polygons, Construction of Regular Polygons, Star Polygons, Discovering Theorems About Polygons.
4. Patterns of Polygons. Tessellations.
Introduction, Tessellations of Polygons, Tessellations with Regular Polygons, Analysis of Semi-Regular Tessellations, Three-Mirror Kaleidoscope, Tessellations of Curved Patterns.
5. Geometry in 3-Dimensions.
Introduction, Regular Polyhedra, Symmetry in Space, Semi-Regular Polyhedra, Tessellations of Space
6. Measurement--Length, Area, and Volume.
Introduction, Need for Standard Units in Measuring, Metric System of Measuring Units, Measuring Length, Measuring Area, Measuring Volume and Capacity, Measuring Mass and Weight.
7. Motions in Geometry.
Introduction, Slides or Translations, Turns or Rotations, Flips or Reflections, Combining Slides, Turns, and Flips, Motions and Congruence.
8. Magnification and Similarity.
Introduction, Magnification, Properties of Magnifications, Similarity.
9. Topology.
Introduction, Topological Equivalence, Networks, Jordan Curve Theorem, Contiguous Regions, Four Color Problem.
10. Number Patterns in Geometry.
Introduction, Patterns of Points, Patterns of Lines, Pattern and Proof, Pascal's Triangle and Related Patterns.
Appendices.
Using Logo in Geometry, Constructions, Metric Units, Critical Thinking, Computer Explorations in Geometry, Glossary, Postulates, and Theorems.
Introduction, Geometry in the Physical World, Geometry as a Mathematical System, Geometry as a Formal Axiomatic Structure, Aesthetic and Recreational Aspects of Geometry, Summary.
2. Basic Ideas of Geometry.
Introduction, Points, Lines, and Their Relationships, Basic Geometric Figures and Their Measures, Line and Angle Relationships, More about Triangles and Quadrilaterals.
3. Discovering Polygon Relationships.
Introduction, More About Polygons, Symmetry of Polygons, Construction of Regular Polygons, Star Polygons, Discovering Theorems About Polygons.
4. Patterns of Polygons. Tessellations.
Introduction, Tessellations of Polygons, Tessellations with Regular Polygons, Analysis of Semi-Regular Tessellations, Three-Mirror Kaleidoscope, Tessellations of Curved Patterns.
5. Geometry in 3-Dimensions.
Introduction, Regular Polyhedra, Symmetry in Space, Semi-Regular Polyhedra, Tessellations of Space
6. Measurement--Length, Area, and Volume.
Introduction, Need for Standard Units in Measuring, Metric System of Measuring Units, Measuring Length, Measuring Area, Measuring Volume and Capacity, Measuring Mass and Weight.
7. Motions in Geometry.
Introduction, Slides or Translations, Turns or Rotations, Flips or Reflections, Combining Slides, Turns, and Flips, Motions and Congruence.
8. Magnification and Similarity.
Introduction, Magnification, Properties of Magnifications, Similarity.
9. Topology.
Introduction, Topological Equivalence, Networks, Jordan Curve Theorem, Contiguous Regions, Four Color Problem.
10. Number Patterns in Geometry.
Introduction, Patterns of Points, Patterns of Lines, Pattern and Proof, Pascal's Triangle and Related Patterns.
Appendices.
Using Logo in Geometry, Constructions, Metric Units, Critical Thinking, Computer Explorations in Geometry, Glossary, Postulates, and Theorems.