skip to content
The four pillars of geometry Preview this item
ClosePreview this item
Checking...

The four pillars of geometry

Author: John Stillwell
Publisher: New York : Springer, ©2005.
Series: Undergraduate texts in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"The Four Pillars of Geometry approaches geometry in four different ways, devoting two chapters to each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Textbooks
Additional Physical Format: Print version:
Stillwell, John.
Four pillars of geometry.
New York : Springer, ©2005
(DLC) 2005929630
(OCoLC)74809803
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John Stillwell
ISBN: 9780387290522 0387290524 0387255303 9780387255309
OCLC Number: 209834142
Description: 1 online resource (xi, 227 pages) : illustrations.
Contents: Preface --
1. Straightedge and compass --
1.1. Euclid's construction axioms --
1.2. Euclid's construction of the equilateral triangle --
1.3. Some basic constructions --
1.4. Multiplication and division--
1.5. Similar triangles --
1.6. Discussion --
2. Euclid's approach to geometry --
2.1. The parallel axiom --
2.2. Congruence axioms --
2.3. Area and equality --
2.4. Area of parallelograms and triangles --
2.5. The Pythagorean theorem --
2.6. Proof of the Thales theorem --
2.7. Angles in a circle --
2.8. The Pythagorean theorem revisited --
2.9. Discussion --
3. Coordinates --
3.1. The number line and the number plane --
3.2. Lines and their equations --
3.3. Distance --
3.4. Intersections of lines and circles --
3.5. Angle and slope --
3.6. Isometries --
3.7. The three reflections theorem --
3.8. Discussion --
4. Vectors and euclidean spaces --
4.1. Vectors --
4.2. Direction and linear independence --
4.3. Midpoints and centroids --
4.4. The inner product --
4.5. Inner product and cosine --
4.6. The triangle inequality --
4.7. Rotations, matrices, and complex numbers --
4.8. Discussion. 5. Perspective --
6.1. Perspective drawing --
5.2. Drawing with straightedge alone --
5.3. Projective plane axioms and their models --
5.4. Homogeneous coordinates --
5.5. Projection --
5.6. Linear fractional functions --
5.7. The cross-ratio --
5.8. What is special about the cross-ratio? --
5.9. Discussion --
6. Projective planes --
6.1. Pappus and Desargues revisited --
6.2. Coincidences --
6.3. Variations on the Desargues theorem --
6.4. Projective arithmetic --
6.5. The field axioms --
6.6. The associative laws --
6.7. The distributive law --
6.8. Discussion --
7. Transformations --
7.1. The group of isometries of the plane --
7.2. Vector transformations --
7.3. Transformations of the projective line --
7.4. Spherical geometry --
7.5. The rotation group of the sphere --
7.6. Representing space rotations by quaternions --
7.7. A finite group of space rotations --
7.8. The group S³ and RP³ --
7.9. Discussion --
8. Non-Euclidean geometry --
8.1. Extending the projective line to a plane --
8.2. Complex conjugation --
8.3. Reflections and Möbius transformations --
8.4. Preserving non-Euclidean lines --
8.5. Preserving angle --
8.6. Non-Euclidean distance --
8.7. Non-Euclidean translations and rotations --
8.8. Three reflections or two involutions --
8.9. Discussion --
References --
Index.
Series Title: Undergraduate texts in mathematics.
Responsibility: John Stillwell.
More information:

Abstract:

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariantsApproach makes the subject  Read more...

Reviews

Editorial reviews

Publisher Synopsis

From the reviews:"This is an introductory book on geometry, easy to read, written in an engaging style. The author's goal is ... to increase one's overall understanding and appreciation of the Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/209834142> # The four pillars of geometry
    a schema:CreativeWork, schema:Book, schema:MediaObject ;
    library:oclcnum "209834142" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
    library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
    schema:about <http://experiment.worldcat.org/entity/work/data/176665#Topic/meetkunde> ; # Meetkunde
    schema:about <http://experiment.worldcat.org/entity/work/data/176665#Topic/mathematics> ; # Mathematics
    schema:about <http://experiment.worldcat.org/entity/work/data/176665#Topic/linear_and_multilinear_algebras_matrix_theory> ; # Linear and Multilinear Algebras, Matrix Theory
    schema:about <http://experiment.worldcat.org/entity/work/data/176665#Topic/matrix_theory> ; # Matrix theory
    schema:about <http://dewey.info/class/516/e22/> ;
    schema:about <http://id.loc.gov/authorities/subjects/sh85054133> ; # Geometry
    schema:about <http://id.worldcat.org/fast/940864> ; # Geometry
    schema:bookFormat schema:EBook ;
    schema:copyrightYear "2005" ;
    schema:creator <http://viaf.org/viaf/14832663> ; # John Stillwell
    schema:datePublished "2005" ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/176665> ;
    schema:genre "Textbooks"@en ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/176665#Series/undergraduate_texts_in_mathematics> ; # Undergraduate texts in mathematics.
    schema:isSimilarTo <http://www.worldcat.org/oclc/74809803> ;
    schema:name "The four pillars of geometry"@en ;
    schema:productID "209834142" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/209834142#PublicationEvent/new_york_springer_2005> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/176665#Agent/springer> ; # Springer
    schema:reviews <http://www.worldcat.org/title/-/oclc/209834142#Review/-1158827034> ;
    schema:url <http://site.ebrary.com/id/10228699> ;
    schema:url <http://swbplus.bsz-bw.de/bsz264335414cov.htm> ;
    schema:url <https://link.springer.com/openurl?genre=book&isbn=978-0-387-25530-9> ;
    schema:url <http://link.springer.com/10.1007/0-387-29052-4> ;
    schema:url <http://rave.ohiolink.edu/ebooks/ebc/0387290524> ;
    schema:url <http://catdir.loc.gov/catdir/enhancements/fy0814/2005929630-t.html> ;
    schema:url <http://www.myilibrary.com?id=133488> ;
    schema:url <https://ebookcentral.proquest.com/lib/stanford-ebooks/detail.action?docID=302807> ;
    schema:url <http://link.springer.com/openurl?genre=book&isbn=978-0-387-25530-9> ;
    schema:url <http://www.springerlink.com/openurl.asp?genre=book&isbn=978-0-387-25530-9> ;
    schema:url <http://dx.doi.org/10.1007/0-387-29052-4> ;
    schema:workExample <http://dx.doi.org/10.1007/0-387-29052-4> ;
    schema:workExample <http://worldcat.org/isbn/9780387255309> ;
    schema:workExample <http://worldcat.org/isbn/9780387290522> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/209834142> ;
    .


Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
    schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/176665#Series/undergraduate_texts_in_mathematics> # Undergraduate texts in mathematics.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/209834142> ; # The four pillars of geometry
    schema:name "Undergraduate texts in mathematics." ;
    .

<http://experiment.worldcat.org/entity/work/data/176665#Topic/linear_and_multilinear_algebras_matrix_theory> # Linear and Multilinear Algebras, Matrix Theory
    a schema:Intangible ;
    schema:name "Linear and Multilinear Algebras, Matrix Theory"@en ;
    .

<http://id.loc.gov/authorities/subjects/sh85054133> # Geometry
    a schema:Intangible ;
    schema:name "Geometry"@en ;
    .

<http://id.worldcat.org/fast/940864> # Geometry
    a schema:Intangible ;
    schema:name "Geometry"@en ;
    .

<http://viaf.org/viaf/14832663> # John Stillwell
    a schema:Person ;
    schema:familyName "Stillwell" ;
    schema:givenName "John" ;
    schema:name "John Stillwell" ;
    .

<http://worldcat.org/isbn/9780387255309>
    a schema:ProductModel ;
    schema:isbn "0387255303" ;
    schema:isbn "9780387255309" ;
    .

<http://worldcat.org/isbn/9780387290522>
    a schema:ProductModel ;
    schema:isbn "0387290524" ;
    schema:isbn "9780387290522" ;
    .

<http://www.worldcat.org/oclc/74809803>
    a schema:CreativeWork ;
    rdfs:label "Four pillars of geometry." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/209834142> ; # The four pillars of geometry
    .

<http://www.worldcat.org/title/-/oclc/209834142#Review/-1158827034>
    a schema:Review ;
    schema:itemReviewed <http://www.worldcat.org/oclc/209834142> ; # The four pillars of geometry
    schema:reviewBody ""The Four Pillars of Geometry approaches geometry in four different ways, devoting two chapters to each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line." "All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers."--Jacket." ;
    .

<https://ebookcentral.proquest.com/lib/stanford-ebooks/detail.action?docID=302807>
    rdfs:comment "Available to Stanford-affiliated users." ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.