國立虎尾科技大學 |

Euclidean, non-Euclidean, and transformational geometry = a deductive inquiry /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Euclidean, non-Euclidean, and transformational geometry/ by Shlomo Libeskind, Isa S. Jubran.
Reminder of title:	a deductive inquiry /
Author:	Libeskind, Shlomo.
other author:	Jubran, Isa S.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xi, 676 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Geometry. -
Online resource:	https://doi.org/10.1007/978-3-031-74153-1
ISBN:	9783031741531

Euclidean, non-Euclidean, and transformational geometry = a deductive inquiry /
Libeskind, Shlomo.

Euclidean, non-Euclidean, and transformational geometrya deductive inquiry /[electronic resource] :by Shlomo Libeskind, Isa S. Jubran. - Cham :Springer International Publishing :2024. - xi, 676 p. :ill., digital ;24 cm.

Preface -- 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.

This 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.

ISBN: 9783031741531

Standard No.: 10.1007/978-3-031-74153-1doiSubjects--Topical Terms:

579899
Geometry.

LC Class. No.: QA445

Dewey Class. No.: 516

Euclidean, non-Euclidean, and transformational geometry = a deductive inquiry /
LDR:03653nam a2200349 a 4500 001 1138452
003 DE-He213
005 20241023125753.0
006 m d
007 cr nn 008maaau
008 250117s2024 sz s 0 eng d
020 $a 9783031741531 $q (electronic bk.)
020 $a 9783031741524 $q (paper)
024 7 $a 10.1007/978-3-031-74153-1 $2 doi
035 $a 978-3-031-74153-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA445
072 7 $a PBM $2 bicssc
072 7 $a PBD $2 bicssc
072 7 $a MAT012020 $2 bisacsh
072 7 $a PBM $2 thema
072 7 $a PBD $2 thema
082 0 4 $a 516 $2 23
090 $a QA445 $b .L695 2024
100 1 $a Libeskind, Shlomo. $3 1462172
245 1 0 $a Euclidean, non-Euclidean, and transformational geometry $h [electronic resource] : $b a deductive inquiry / $c by Shlomo Libeskind, Isa S. Jubran.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2024.
300 $a xi, 676 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- 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 $a This 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 $a Geometry. $3 579899
650 0 $a Euclid's Elements. $3 1070497
650 1 4 $a Convex and Discrete Geometry. $3 672138
650 2 4 $a Projective Geometry. $3 1021390
650 2 4 $a Hyperbolic Geometry. $3 1069789
700 1 $a Jubran, Isa S. $3 1462173
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-74153-1
950 $a Mathematics and Statistics (SpringerNature-11649)