Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others]

• Pubblicazione: Hoboken, New Jersey : , : Wiley, , 2014; ©2014
• Edizione: 1st edition
• Descrizione fisica: 1 online resource (493 p.)
• Disciplina: 516
• Soggetto topico: Geometry
• Soggetto genere / forma: Electronic books.
• Classificazione: MAT012000EDU027000MAT003000
• Persona (resp. second.): LeonardI. Ed. <1938->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: CLASSICAL 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 ; 2.6 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 ; 4.7 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 ; 6.7 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 ; 9.3 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 ; PART Ill INVERSIVE AND PROJECTIVE GEOMETRIES
• Sommario/riassunto: "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"--
• Titolo autorizzato: Classical geometry
• ISBN: 1-118-67914-8; 1-118-83943-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910464443603321
• Lo trovi qui: Univ. Federico II