INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
0387255303 (acid-free paper)
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-53344
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
The four pillars of geometry
General Material Designation
[Book]
First Statement of Responsibility
/ John Stillwell
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York
Name of Publisher, Distributor, etc.
: Springer,
Date of Publication, Distribution, etc.
, c2005.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
xi, 227 p. , ill. , 25 cm.
SERIES
Series Title
(Undergraduate texts in mathematics.)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references (p. 213-214) and index.
CONTENTS NOTE
Text of Note
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 --
Text of Note
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 SooAلآ and RPooAلآ -- 7.9. Discussion -- 8. Non-Euclidean geometry -- 8.1. Extending the projective line to a plane -- 8.2. Complex conjugation -- 8.3. Reflections and Mobius 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.
TOPICAL NAME USED AS SUBJECT
Geometry , Textbooks
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Stillwell, John.
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9780387255309.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9780387255309.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
