LEADER 04736nam 22006975 450 001 9910897978603321 005 20260121094931.0 010 $a9783031741531 010 $a3031741536 024 7 $a10.1007/978-3-031-74153-1 035 $a(MiAaPQ)EBC31735756 035 $a(Au-PeEL)EBL31735756 035 $a(CKB)36389375900041 035 $a(DE-He213)978-3-031-74153-1 035 $a(EXLCZ)9936389375900041 100 $a20241023d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEuclidean, Non-Euclidean, and Transformational Geometry $eA Deductive Inquiry /$fby Shlomo Libeskind, Isa S. Jubran 205 $a1st ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (680 pages) 311 08$a9783031741524 311 08$a3031741528 320 $aIncludes bibliographical references and index. 327 $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. 330 $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. 606 $aConvex geometry 606 $aDiscrete geometry 606 $aGeometry, Projective 606 $aGeometry, Hyperbolic 606 $aConvex and Discrete Geometry 606 $aProjective Geometry 606 $aHyperbolic Geometry 606 $aGeometria discreta$2thub 606 $aGeometria convexa$2thub 606 $aGeometria hiperbòlica$2thub 608 $aLlibres electrònics$2thub 615 0$aConvex geometry. 615 0$aDiscrete geometry. 615 0$aGeometry, Projective. 615 0$aGeometry, Hyperbolic. 615 14$aConvex and Discrete Geometry. 615 24$aProjective Geometry. 615 24$aHyperbolic Geometry. 615 7$aGeometria discreta 615 7$aGeometria convexa 615 7$aGeometria hiperbòlica 676 $a516.22 700 $aLibeskind$b Shlomo$01766770 702 $aJubran$b Isa S. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897978603321 996 $aEuclidean, Non-Euclidean, and Transformational Geometry$94211492 997 $aUNINA