At the college level, Geometry is not taught for its applications. It is taught either for its beauty, or as a way to teach proof techniques and systems of axioms. In this book, it is the latter concept that prevails. Students who already had a course on proofs will not need these chapters. The book ends with an extensive Appendix, in which systems of axioms dominate one more time.
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At the college level, Geometry is not taught for its applications. It is taught either for its beauty, or as a way to teach proof techniques and systems of axioms. In this book, it is the latter concept that prevails. Students who already had a course on proofs will not need these chapters. The book ends with an extensive Appendix, in which systems of axioms dominate one more time. Besides various geometric systems of axioms, there is also an introduction to set theory.
The main audience for the book seems to be a class whose goal is to teach students the concept of proofs using geometry as the main avenue. Readers who do not fall into that category may still enjoy the classic, but perhaps universally known results covered in Chapter 8. Skip to main content. Search form Search. Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Gerard A. Publication Date:. Number of Pages:. Axiomatic Systems and Incidence Geometry 2. Axioms for Plane Geometry 3.
Neutral Geometry 4. Euclidean Geometry 5. Hyperbolic Geometry 6. Area 7. Circles 8. Constructions 9. Transformations Models Polygonal Models and the Geometry of Space Systems of Axioms for Geometry B. The Postulates Used in this Book C. Set Notation and the Real Numbers D. The van Hiele Model F. Hints for Selected Exercises Bibliography Index. Euclidean Geometry. Log in to post comments.
Foundations of Geometry
Foundations of Geometry. Gerard Venema. Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements , lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry.