Coverart for item
The Resource The four pillars of geometry, John Stillwell

The four pillars of geometry, John Stillwell

Label
The four pillars of geometry
Title
The four pillars of geometry
Statement of responsibility
John Stillwell
Creator
Subject
Genre
Language
eng
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 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
Member of
Is part of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Stillwell, John
Dewey number
516
Illustrations
illustrations
Index
index present
LC call number
QA445
LC item number
.S763 2005eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Undergraduate texts in mathematics
http://library.link/vocab/subjectName
  • Geometry
  • Matrix theory
  • Mathematics
  • Geometry
  • Linear and Multilinear Algebras, Matrix Theory
  • Geometry
  • Meetkunde
Label
The four pillars of geometry, John Stillwell
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 213-214) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Some basic constructions
  • 1.4.
  • Multiplication and division--
  • 1.5.
  • Similar triangles
  • 1.6.
  • Discussion
  • 2.
  • Euclid's approach to geometry
  • 2.1.
  • Preface
  • 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.
  • 1.
  • Proof of the Thales theorem
  • 2.7.
  • Angles in a circle
  • 2.8.
  • The Pythagorean theorem revisited
  • 2.9.
  • Discussion
  • 3.
  • Coordinates
  • 3.1.
  • Straightedge and compass
  • 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.
  • 1.1.
  • Isometries
  • 3.7.
  • The three reflections theorem
  • 3.8.
  • Discussion
  • 4.
  • Vectors and euclidean spaces
  • 4.1.
  • Vectors
  • 4.2.
  • Euclid's construction axioms
  • 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.
  • 1.2.
  • Rotations, matrices, and complex numbers
  • 4.8.
  • Discussion
  • Euclid's construction of the equilateral triangle
  • 1.3.
  • 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.
  • 5.9.
  • Discussion
  • 6.
  • Projective planes
  • 6.1.
  • Pappus and Desargues revisited
  • 6.2.
  • Coincidences
  • 6.3.
  • Variations on the Desargues theorem
  • Perspective
  • 6.4.
  • Projective arithmetic
  • 6.5.
  • The field axioms
  • 6.6.
  • The associative laws
  • 6.7.
  • The distributive law
  • 6.8.
  • Discussion
  • 6.1.
  • 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
  • Perspective drawing
  • 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
  • 5.2.
  • 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
  • Drawing with straightedge alone
  • 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
  • 5.3.
  • References
  • Index
  • Projective plane axioms and their models
Control code
209834142
Dimensions
unknown
Extent
1 online resource (xi, 227 pages)
Form of item
online
Isbn
9780387290522
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-387-29052-4
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-25530-9
Specific material designation
remote
System control number
(OCoLC)209834142
Label
The four pillars of geometry, John Stillwell
Publication
Bibliography note
Includes bibliographical references (pages 213-214) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Some basic constructions
  • 1.4.
  • Multiplication and division--
  • 1.5.
  • Similar triangles
  • 1.6.
  • Discussion
  • 2.
  • Euclid's approach to geometry
  • 2.1.
  • Preface
  • 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.
  • 1.
  • Proof of the Thales theorem
  • 2.7.
  • Angles in a circle
  • 2.8.
  • The Pythagorean theorem revisited
  • 2.9.
  • Discussion
  • 3.
  • Coordinates
  • 3.1.
  • Straightedge and compass
  • 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.
  • 1.1.
  • Isometries
  • 3.7.
  • The three reflections theorem
  • 3.8.
  • Discussion
  • 4.
  • Vectors and euclidean spaces
  • 4.1.
  • Vectors
  • 4.2.
  • Euclid's construction axioms
  • 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.
  • 1.2.
  • Rotations, matrices, and complex numbers
  • 4.8.
  • Discussion
  • Euclid's construction of the equilateral triangle
  • 1.3.
  • 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.
  • 5.9.
  • Discussion
  • 6.
  • Projective planes
  • 6.1.
  • Pappus and Desargues revisited
  • 6.2.
  • Coincidences
  • 6.3.
  • Variations on the Desargues theorem
  • Perspective
  • 6.4.
  • Projective arithmetic
  • 6.5.
  • The field axioms
  • 6.6.
  • The associative laws
  • 6.7.
  • The distributive law
  • 6.8.
  • Discussion
  • 6.1.
  • 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
  • Perspective drawing
  • 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
  • 5.2.
  • 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
  • Drawing with straightedge alone
  • 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
  • 5.3.
  • References
  • Index
  • Projective plane axioms and their models
Control code
209834142
Dimensions
unknown
Extent
1 online resource (xi, 227 pages)
Form of item
online
Isbn
9780387290522
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-387-29052-4
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-25530-9
Specific material designation
remote
System control number
(OCoLC)209834142

Library Locations

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      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012
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