EUCLIDEAN AND NON-EUCLIDEAN GEOMETRIES

Euclidean and Non-Euclidean Geometries: Development and History

Marvin J. Greenberg

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This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.

contenido:—-chapter 1 euclid`s geometry—charpe 2 logic and incide geometry—charpe 3 hilbert`s axioms—charpe 4 neutral geometry—charpe 5 history of te parallel postulate—charpe 6 the discovery of non-euclidean geometry—charpe 7 independence of the parallel postulate–charpe 8philosophical implications, fruitful appliccations—-charpe 9 geometric transformations—charpe 10 furthe reslts in real hyperbolic geometry

appendix A — elliptic and other riemanian geometries

appendix B — hilbert`s geometry without real numbers

Axioms

Bibliography

Symbols

Name Index,Subject Index