| 书目名称 | Euclidean Geometry and its Subgeometries | | 编辑 | Edward John Specht,Harold Trainer Jones,Donald H. | | 视频video | | | 概述 | Provides a complete and rigorous axiomatic treatment of Euclidean geometry..Proofs for many theorems are worked out in detail..Takes a modern approach by replacing congruence axioms with a transformat | | 图书封面 |  | | 描述 | In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. .There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online cover | | 出版日期 | Book 2015 | | 关键词 | Betweenness; Euclidean geometry; Euclidean plane; Geometric axioms; Incidence; Least Upper Bound | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-23775-6 | | isbn_softcover | 978-3-319-79533-1 | | isbn_ebook | 978-3-319-23775-6 | | copyright | Springer International Publishing Switzerland 2015 |
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发表于 2025-3-21 19:34:44
