LEADER 05388nam 2200661 450 001 9910464443603321 005 20200520144314.0 010 $a1-118-67914-8 010 $a1-118-83943-9 035 $a(CKB)3710000000125535 035 $a(EBL)1684622 035 $a(SSID)ssj0001226345 035 $a(PQKBManifestationID)11730612 035 $a(PQKBTitleCode)TC0001226345 035 $a(PQKBWorkID)11270254 035 $a(PQKB)10473016 035 $a(MiAaPQ)EBC1684622 035 $a(DLC) 2013043455 035 $a(CaSebORM)9781118679142 035 $a(Au-PeEL)EBL1684622 035 $a(CaPaEBR)ebr10881038 035 $a(CaONFJC)MIL621906 035 $a(OCoLC)861966488 035 $a(EXLCZ)993710000000125535 100 $a20140617h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aClassical geometry $eeuclidean, transformational, inversive, and projective /$fEd I. Leonard, [and three others] 205 $a1st edition 210 1$aHoboken, New Jersey :$cWiley,$d2014. 210 4$dİ2014 215 $a1 online resource (493 p.) 300 $aDescription based upon print version of record. 311 $a1-118-67919-9 320 $aIncludes bibliographical references and index. 327 $aCLASSICAL GEOMETRY: Euclidean, Transformational, Inversive, and Projective; Copyright; CONTENTS; Preface; PART I EUCLIDEAN GEOMETRY; 1 PART I EUCLIDEAN GEOMETRY Congruency; 1.1 Introduction; 1.2 Congruent Figures; 1.3 Parallel Lines; 1.3.1 Angles in a Triangle; 1.3.2 Thales' Theorem; 1.3.3 Quadrilaterals; 1.4 More About Congruency; 1.5 Perpendiculars and Angle Bisectors; 1.6 Construction Problems; 1.6.1 The Method of Loci; 1.7 Solutions to Selected Exercises; 1.8 Problems; 2 Concurrency; 2.1 Perpendicular Bisectors; 2.2 Angle Bisectors; 2.3 Altitudes; 2.4 Medians; 2.5 Construction Problems 327 $a2.6 Solutions to the Exercises2.7 Problems; 3 Similarity; 3.1 Similar Triangles; 3.2 Parallel Lines and Similarity; 3.3 Other Conditions Implying Similarity; 3.4 Examples; 3.5 Construction Problems; 3.6 The Power of a Point; 3.7 Solutions to the Exercises; 3.8 Problems; 4 Theorems of Ceva and Menelaus; 4.1 Directed Distances, Directed Ratios; 4.2 The Theorems; 4.3 Applications of Ceva's Theorem; 4.4 Applications of Menelaus' Theorem; 4.5 Proofs of the Theorems; 4.6 Extended Versions of the Theorems; 4.6.1 Ceva's Theorem in the Extended Plane; 4.6.2 Menelaus' Theorem in the Extended Plane 327 $a4.7 Problems5 Area; 5.1 Basic Properties; 5.1.1 Areas of Polygons; 5.1.2 Finding the Area of Polygons; 5.1.3 Areas of Other Shapes; 5.2 Applications of the Basic Properties; 5.3 Other Formulae for the Area of a Triangle; 5.4 Solutions to the Exercises; 5.5 Problems; 6 Miscellaneous Topics; 6.1 The Three Problems of Antiquity; 6.2 Constructing Segments of Specific Lengths; 6.3 Construction of Regular Polygons; 6.3.1 Construction of the Regular Pentagon; 6.3.2 Construction of Other Regular Polygons; 6.4 Miquel's Theorem; 6.5 Morley's Theorem; 6.6 The Nine-Point Circle; 6.6.1 Special Cases 327 $a6.7 The Steiner-Lehmus Theorem6.8 The Circle of Apollonius; 6.9 Solutions to the Exercises; 6.10 Problems; PART II TRANSFORMATIONAL GEOMETRY; 7 The Euclidean Transformations or lsometries; 7.1 Rotations, Reflections, and Translations; 7.2 Mappings and Transformations; 7.2.1 Isometries; 7.3 Using Rotations, Reflections, and Translations; 7.4 Problems; 8 The Algebra of lsometries; 8.1 Basic Algebraic Properties; 8.2 Groups of Isometries; 8.2.1 Direct and Opposite Isometries; 8.3 The Product of Reflections; 8.4 Problems; 9 The Product of Direct lsometries; 9.1 Angles; 9.2 Fixed Points 327 $a9.3 The Product of Two Translations9.4 The Product of a Translation and a Rotation; 9.5 The Product of Two Rotations; 9.6 Problems; 10 Symmetry and Groups; 10.1 More About Groups; 10.1.1 Cyclic and Dihedral Groups; 10.2 Leonardo's Theorem; 10.3 Problems; 11 Homotheties; 11.1 The Pantograph; 11.2 Some Basic Properties; 11.2.1 Circles; 11.3 Construction Problems; 11.4 Using Homotheties in Proofs; 11.5 Dilatation; 11.6 Problems; 12 Tessellations; 12.1 Tilings; 12.2 Monohedral Tilings; 12.3 Tiling with Regular Polygons; 12.4 Platonic and Archimedean Tilings; 12.5 Problems 327 $aPART Ill INVERSIVE AND PROJECTIVE GEOMETRIES 330 $a"Written by well-known mathematical problem solvers, Modern Geometry features up-to-date and applicable coverage of the wide spectrum of modern geometry and aids readers in learning the art of logical reasoning, modeling, and proof. With its reader-friendly approach, this undergraduate text features: self-contained coverage of modern geometry, provides a large selection of solved exercises to aid in reader comprehension, contains material that can be tailored for a one-, two-, or three-semester sequence, and provides a wide range of fully worked exercises throughout"--$cProvided by publisher. 606 $aGeometry 608 $aElectronic books. 615 0$aGeometry. 676 $a516 686 $aMAT012000$aEDU027000$aMAT003000$2bisacsh 702 $aLeonard$b I. Ed.$f1938- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464443603321 996 $aClassical geometry$91934569 997 $aUNINA