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An IBL Introduction to Geometries
Mark A. Fitch
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Front Matter
Colophon
Acknowledgements
Preface
1
Completeness and Consistency
1.1
Finite Geometries
1.2
Completeness
1.3
Consistency
1.4
Explain and Apply
2
Neutral Geometry
2.1
Triangles
2.1.1
Basic Triangle Theorems
2.1.2
Triangle Congruence Theorems
3
Synthetic Euclidean Geometry
3.1
Equivalent Parallel Postulates
3.1.1
Preparation
3.1.2
Equivalency
3.2
Similarity
3.2.1
Preparation Theorems
3.2.2
Explore Similarity Theorems
3.2.3
Similarity Theorems
3.2.4
Extending Similarity
3.3
Concurrent
3.3.1
Explore
3.3.2
Prove
3.4
Constructions
3.4.1
Discover and Prove Construction
4
Transformational Geometry
4.1
Transformation
4.1.1
Planar Transformations
4.1.2
Isometry
4.1.3
Dilations
4.2
Analytic Transformational Geometry
4.3
Algebra of Transformations
4.3.1
Explore
4.3.2
Prove
4.4
Symmetries
4.4.1
Explore Symmetries
4.4.2
Explore Tesselations
4.4.3
Tesselation Images
5
Hyperbolic Geometry
5.1
Hyperbolic Geometry
5.2
A Model for Hyperbolic Geometry
5.3
Theorems of Hyperbolic Geometry
5.4
Parallels in Hyperbolic
6
Projective Geometry
6.1
Axioms for Projective Geometry
6.1.1
Motivating Illustration
6.1.2
Axioms for Projective Geometry
6.1.3
Duality
6.2
Perspectivities
Back Matter
A
Glossary
B
SMSG Axioms
Acknowledgements
Acknowledgements
This problem set was developed for the MATH A305 Introduction to Geometries at the University of Alaska Anchorage. It has been modified based on the experience of the students in this class.
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