Umfang:
Online-Ressource (PDF-Dateien: XI, 497 Seiten) :
,
Illustrationen, Diagramme.
Ausgabe:
Eighth printing 2007, transferred to digital printing 2009
ISBN:
978-0-511-80750-3
,
978-1-139-00300-1
Inhalt:
"This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831"--
Anmerkung:
Frontmatter: "Online publication date: June 2012". - Differences between the printed and electronic version of the document are possible. - Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden
,
Geometry and Geometries""; ""1 Conics""; ""1.1 Conic Sections and Conics""; ""1.1.1 Conic Sections""; ""1.1.2 Circles""; ""Orthogonal Circles""; ""Circles through Two Points""; ""1.1.3 Focus-Directrix Definition of the Non-Degenerate Conics""; ""Parabola""; ""Ellipse""; ""Hyperbola""; ""Rectangular Hyperbola""
,
""Polar Equation of a Conic""""1.1.4 Focal Distance Properties of Ellipse and Hyperbola""; ""1.1.5 Dandelin Spheres""; ""1.2 Properties of Conics""; ""1.2.1 Tangents""; ""1.2.2 Reflections""; ""Reflection Property of the Ellipse""; ""Reflection Property of the Hyperbola""; ""Reflection Property of the Parabola""; ""1.2.3 Conics as envelopes of tangent families""; ""Parabola""; ""Ellipse""; ""Hyperbola""; ""1.3 Recognizing Conics""; ""Introducing Matrices""; ""Using Matrices""; ""1.4 Quadric Surfaces""; ""1.4.1 Quadric Surfaces in R3""; ""1.4.2 Recognizing Quadric Surfaces""
,
""Introducing Matrices""""Using Matrices""; ""1.4.3 Rulings of Quadric Surfaces""; ""The Hyperboloid of One Sheet""; ""The Hyperbolic Paraboloid""; ""1.5 Exercises""; ""Summary of Chapter 1""; ""2 Affine Geometry""; ""2.1 Geometry and Transformations""; ""2.1.1 What is Euclidean Geometry?""; ""2.1.2 Euclidean-Congruence""; ""2.2 Affine Transformations and Parallel Projections ""; ""2.2.1 Affine Transformations""; ""2.2.2 Parallel Projections""; ""2.2.3 Affine Geometry""; ""Two Results about Ellipses""; ""Proofs for the Special Case of a Circle""; ""Generalizing the Proof""
,
""Affine Transformations and Parallel Projections""""2.3 Properties of Affine Transformations""; ""2.3.1 Images of Sets Under Affine Transformations""; ""2.3.2 The Fundamental Theorem of Affine Geometry""; ""2.3.3 Proofs of the Basic Properties of Affine Transformations""; ""2.4 Using the Fundamental Theorem of Affine Geometry""; ""2.4.1 The Median Theorem""; ""2.4.2 Ceva's Theorem""; ""2.4.3 Menelaus' Theorem""; ""2.4.4 Barycentric Coordinates""; ""2.5 Affine Transformations and Conics""; ""2.5.1 Classifying Non-Degenerate Conics in Affine Geometry""
,
Lines""; ""3.1 Perspective""; ""3.1.1 Perspective in Art""; ""3.1.2 Mathematical Perspective""; ""3.1.3 Desargues' Theorem""; ""3.2 The Projective Plane RP2""; ""3.2.1 Projective Points""; ""3.2.2 Projective Lines""; ""3.2.3 Embedding Planes""; ""3.2.4 An equivalent definition of Projective Geometry""; ""3.3 Projective Transformations""; ""3.3.1 The Group of Projective Transformations""; ""3.3.2 Some Properties of Projective Transformations""
,
""3.3.3 Fundamental Theorem of Projective Geometry""
,
Includes index
,
Literaturverz. S. 490 - 491
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 978-1-10-764783-1
Weitere Ausg.:
ISBN 1-10-764783-5
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe, Hardcover 1999 ISBN 978-0-521-59193-5
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe, Paperback 1999 ISBN 978-0-521-59787-6
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Geometrie
;
Lehrbuch
;
Lehrbuch
DOI:
10.1017/CBO9781139003001
Mehr zum Autor:
Gray, Jeremy J. 1947-
