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001 978-3-031-74153-1
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020 _a9783031741531
_9978-3-031-74153-1
024 7 _a10.1007/978-3-031-74153-1
_2doi
050 4 _aQA639.5-640.7
050 4 _aQA640.7-640.77
072 7 _aPBM
_2bicssc
072 7 _aPBD
_2bicssc
072 7 _aMAT012020
_2bisacsh
072 7 _aPBM
_2thema
072 7 _aPBD
_2thema
100 1 _aLibeskind, Shlomo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986487
245 1 0 _aEuclidean, Non-Euclidean, and Transformational Geometry
_h[electronic resource] :
_bA Deductive Inquiry /
_cby Shlomo Libeskind, Isa S. Jubran.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2024.
300 _aXI, 676 p. 620 illus., 614 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Surprising Results and Basic Notions -- Congruence, Constructions, and the Parallel Postulate -- Circles -- Area and the Pythagorean Theorem -- Similarity -- Isometries and Size Transformations -- Composition of Transformations -- More Recent Discoveries -- Inversion -- Hyperbolic Geometry -- Elliptic Geometries -- Projective Geometry -- Taxicab Geometry -- Fractal Geometry -- Solid Geometry.
520 _aThis undergraduate textbook provides a comprehensive treatment of Euclidean and transformational geometries, supplemented by substantial discussions of topics from various non-Euclidean and less commonly taught geometries, making it ideal for both mathematics majors and pre-service teachers. Emphasis is placed on developing students' deductive reasoning skills as they are guided through proofs, constructions, and solutions to problems. The text frequently emphasizes strategies and heuristics of problem solving including constructing proofs (Where to begin? How to proceed? Which approach is more promising? Are there multiple solutions/proofs? etc.). This approach aims not only to enable students to successfully solve unfamiliar problems on their own, but also to impart a lasting appreciation for mathematics. The text first explores, at a higher level and in much greater depth, topics that are normally taught in high school geometry courses: definitions and axioms, congruence, circles and related concepts, area and the Pythagorean theorem, similarity, isometries and size transformations, and composition of transformations. Constructions and the use of transformations to carry out constructions are emphasized. The text then introduces more advanced topics dealing with non-Euclidean and less commonly taught topics such as inversive, hyperbolic, elliptic, taxicab, fractal, and solid geometries. By examining what happens when one or more of the building blocks of Euclidean geometry are altered, students will gain a deeper understanding of and appreciation for Euclidean concepts. To accommodate students with different levels of experience in the subject, the basic definitions and axioms that form the foundation of Euclidean geometry are covered in Chapter 1. Problem sets are provided after every section in each chapter and include nonroutine problems that students will enjoy exploring. While not necessarily required, the appropriate use of freely available dynamic geometry software and other specialized software referenced in the text is strongly encouraged; this is especially important for visual learners and for forming conjectures and testing hypotheses.
650 0 _aConvex geometry .
_971929
650 0 _aDiscrete geometry.
_971930
650 0 _aProjective geometry.
650 0 _aGeometry, Hyperbolic.
_980110
650 1 4 _aConvex and Discrete Geometry.
_971931
650 2 4 _aProjective Geometry.
650 2 4 _aHyperbolic Geometry.
_980111
700 1 _aJubran, Isa S.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986488
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031741524
776 0 8 _iPrinted edition:
_z9783031741548
776 0 8 _iPrinted edition:
_z9783031741555
856 4 0 _uhttps://doi.org/10.1007/978-3-031-74153-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c64428
_d64428