Verfügbarkeit: Geometry :: THWS Bibkatalog

Geometry:

"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,...

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Bibliographische Detailangaben
Hauptverfasser:	Brannan, David A. (VerfasserIn), Esplen, Matthew F. (VerfasserIn), Gray, Jeremy J. 1947- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2012
Ausgabe:	Eighth printing 2007, transferred to digital printing 2009
Schlagworte:	Geometrie Geometry Lehrbuch
Online-Zugang:	FUBA1 Volltext
Zusammenfassung:	"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"--
Beschreibung:	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
Beschreibung:	Online-Ressource (PDF-Dateien: XI, 497 Seiten) Illustrationen, Diagramme
ISBN:	9780511807503 9781139003001
DOI:	10.1017/CBO9781139003001

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245	1	0	\|a Geometry \|c David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray, The Open University
250			\|a Eighth printing 2007, transferred to digital printing 2009
264		1	\|a Cambridge [u.a.] \|b Cambridge Univ. Press \|c 2012
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505	8		\|a 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""
505	8		\|a ""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""
505	8		\|a ""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""
505	8		\|a ""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""
505	8		\|a 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""
505	8		\|a ""3.3.3 Fundamental Theorem of Projective Geometry""
505	8		\|a Includes index
505	8		\|a Literaturverz. S. 490 - 491
520	3		\|a "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"--
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700	1		\|a Esplen, Matthew F. \|e Verfasser \|0 (DE-588)1023547031 \|4 aut
700	1		\|a Gray, Jeremy J. \|d 1947- \|e Verfasser \|0 (DE-588)122175549 \|4 aut
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Datensatz im Suchindex

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author	Brannan, David A. Esplen, Matthew F. Gray, Jeremy J. 1947-
author_GND	(DE-588)131109871 (DE-588)1023547031 (DE-588)122175549
author_facet	Brannan, David A. Esplen, Matthew F. Gray, Jeremy J. 1947-
author_role	aut aut aut
author_sort	Brannan, David A.
author_variant	d a b da dab m f e mf mfe j j g jj jjg
building	Verbundindex
bvnumber	BV046694493
callnumber-first	Q - Science
callnumber-label	QA445
callnumber-raw	QA445
callnumber-search	QA445
callnumber-sort	QA 3445
callnumber-subject	QA - Mathematics
classification_rvk	SK 380
collection	ZDB-20-CBO
contents	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
ctrlnum	(OCoLC)1261747483 (DE-599)GBV721879543
dewey-full	516
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	516 - Geometry
dewey-raw	516
dewey-search	516
dewey-sort	3516
dewey-tens	510 - Mathematics
discipline	Mathematik
discipline_str_mv	Mathematik
doi_str_mv	10.1017/CBO9781139003001
edition	Eighth printing 2007, transferred to digital printing 2009
format	Electronic eBook
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genre	(DE-588)4123623-3 Lehrbuch gnd-content
genre_facet	Lehrbuch
id	DE-604.BV046694493
illustrated	Not Illustrated
index_date	2024-07-03T14:26:09Z
indexdate	2024-07-10T08:51:19Z
institution	BVB
isbn	9780511807503 9781139003001
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-032105181
oclc_num	1261747483
open_access_boolean
owner	DE-188
owner_facet	DE-188
physical	Online-Ressource (PDF-Dateien: XI, 497 Seiten) Illustrationen, Diagramme
psigel	ZDB-20-CBO H-ZDB-38-EBR H-ZDB-30-PQE H-ZDB-32-STB H-GBV-EBRARY-UBCL H-GBV-Safari-alles
publishDate	2012
publishDateSearch	2012
publishDateSort	2012
publisher	Cambridge Univ. Press
record_format	marc
spelling	Brannan, David A. Verfasser (DE-588)131109871 aut Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray, The Open University Eighth printing 2007, transferred to digital printing 2009 Cambridge [u.a.] Cambridge Univ. Press 2012 Online-Ressource (PDF-Dateien: XI, 497 Seiten) Illustrationen, Diagramme zzz rdacontent c rdamedia cr rdacarrier 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 "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"-- Geometrie (DE-588)4020236-7 gnd rswk-swf Geometry (DE-588)4123623-3 Lehrbuch gnd-content Geometrie (DE-588)4020236-7 s 1\p DE-604 Esplen, Matthew F. Verfasser (DE-588)1023547031 aut Gray, Jeremy J. 1947- Verfasser (DE-588)122175549 aut Erscheint auch als Druck-Ausgabe 978-1-10-764783-1 1-10-764783-5 Erscheint auch als Druck-Ausgabe, Hardcover 1999 978-0-521-59193-5 Erscheint auch als Druck-Ausgabe, Paperback 1999 978-0-521-59787-6 https://doi.org/10.1017/CBO9781139003001 Resolving-System E-books (Cambridge University Press) Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Brannan, David A. Esplen, Matthew F. Gray, Jeremy J. 1947- Geometry 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 Geometrie (DE-588)4020236-7 gnd
subject_GND	(DE-588)4020236-7 (DE-588)4123623-3
title	Geometry
title_auth	Geometry
title_exact_search	Geometry
title_exact_search_txtP	Geometry
title_full	Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray, The Open University
title_fullStr	Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray, The Open University
title_full_unstemmed	Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray, The Open University
title_short	Geometry
title_sort	geometry
topic	Geometrie (DE-588)4020236-7 gnd
topic_facet	Geometrie Lehrbuch
url	https://doi.org/10.1017/CBO9781139003001
work_keys_str_mv	AT brannandavida geometry AT esplenmatthewf geometry AT grayjeremyj geometry

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