An IBL Introduction to Geometries

by Mark A. Fitch

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This text was designed for an IBL approach to Introduction to Geometries and covers geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and a tiny bit of analytic approaches to geometry and covers both Euclidean (parabolic), hyperbolic, and some projective geometry. Students are expected to have completed a proofs course covering proof techniques, basic set operations, and cardinality as a prerequisite.

Description from LibreTexts.

Publisher
University of Alaska Anchorage
Subjects
Mathematics, Geometry
Licence
GNU Free Documentation License, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Completeness and Consistency
  7. 1.1: Finite Geometries
  8. 1.2: Completeness
  9. 1.3: Consistency
  10. 1.4: Explain and Apply
  11. 2: Neutral Geometry
  12. 2.1: Triangles
  13. 3: Synthetic Euclidean Geometry
  14. 3.1: Equivalent Parallel Postulates
  15. 3.2: Similarity
  16. 3.3: Concurrent
  17. 3.4: Constructions
  18. 4: Transformational Geometry
  19. 4.1: Transformation
  20. 4.2: Analytic Transformational Geometry
  21. 4.3: Algebra of Transformations
  22. 4.4: Symmetries
  23. 5: Hyperbolic Geometry
  24. 5.1: Hyperbolic Geometry
  25. 5.2: A Model for Hyperbolic Geometry
  26. 5.3: Theorems of Hyperbolic Geometry
  27. 5.4: Parallels in Hyperbolic
  28. 6: Projective Geometry
  29. 6.1: Axioms for Projective Geometry
  30. 6.2: Perspectivities
  31. Back Matter
  32. Index
  33. Glossary
  34. Detailed Licensing