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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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Edition: | Eighth printing 2007, transferred to digital printing 2009 |
| Subjects: | |
| Online Access: | FUBA1 Volltext |
| Summary: | "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"-- |
| Item Description: | 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 |
| Physical Description: | Online-Ressource (PDF-Dateien: XI, 497 Seiten) Illustrationen, Diagramme |
| ISBN: | 9780511807503 9781139003001 |
| DOI: | 10.1017/CBO9781139003001 |
Staff View
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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 | |
| 300 | |a Online-Ressource (PDF-Dateien: XI, 497 Seiten) |b Illustrationen, Diagramme | ||
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| 500 | |a Frontmatter: "Online publication date: June 2012" | ||
| 500 | |a Differences between the printed and electronic version of the document are possible | ||
| 500 | |a Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden | ||
| 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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| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |d 1999 |z 978-0-521-59787-6 |
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Record in the Search Index
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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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Press</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">Online-Ressource (PDF-Dateien: XI, 497 Seiten)</subfield><subfield code="b">Illustrationen, Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Frontmatter: "Online publication date: June 2012"</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Differences between the printed and electronic version of the document are possible</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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""</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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""</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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""</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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""</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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""</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">""3.3.3 Fundamental Theorem of Projective Geometry""</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Includes index</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Literaturverz. S. 490 - 491</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="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"--</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Geometry</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Esplen, Matthew F.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1023547031</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gray, Jeremy J.</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122175549</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-1-10-764783-1</subfield><subfield code="z">1-10-764783-5</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Hardcover</subfield><subfield code="d">1999</subfield><subfield code="z">978-0-521-59193-5</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="d">1999</subfield><subfield code="z">978-0-521-59787-6</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781139003001</subfield><subfield code="x">Resolving-System</subfield><subfield code="y">E-books (Cambridge University Press)</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">H-ZDB-38-EBR</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">H-ZDB-30-PQE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">H-ZDB-32-STB</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">H-GBV-EBRARY-UBCL</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">H-GBV-Safari-alles</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032105181</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139003001</subfield><subfield code="l">FUBA1</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| 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 |