Plane and solid geometry:
"The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry as well as to...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Dutch |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Zusammenfassung: | "The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry as well as tools for other subjects."--Back cover |
| Beschreibung: | Aus dem Niederländ. übers. |
| Beschreibung: | XIV, 349 S. graph. Darst. |
| ISBN: | 9780387782409 9780387782416 |
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Datensatz im Suchindex
| _version_ | 1805091190755819520 |
|---|---|
| adam_text |
Contents
1 PLANE
GEOMETRY
. 1
1.1
The Pythagorean Theorem
. 2
Exercises
. 7
1.2
Metrics and Metric Spaces
. 8
Exercises
. 10
1.3
Isometries
. 11
Exercises
. 14
1.4
The Basic Assumptions of Plane Geometry
. 15
Exercises
. 22
1.5
Local Coordinates and the Equation of a Line
. 22
Exercises
. 30
1.6
The Inner Product and Determinant
. 31
Exercises
. 36
2
TRANSFORMATIONS
. 37
2.1
The Reflection in a Line, Congruence
. 38
Exercises
. 44
2.2
Angle Measure, Orientation
. 45
Exercises
. 53
2.3
The Reflection in a Point
. 53
Exercises
. 60
2.4
Translation and Rotation Groups
. 61
Exercises
. 75
2.5
Dilation and Similarity
. 76
Exercises
. 84
2.6
Fractals, Dimension, and Measure
. 86
Exercises
. 93
3
SYMMETRY
. 95
3.1
What Is Symmetry?
. 96
Exercises
. 101
xiv Contents
3.2
There Are Seven Types of Frieze Patterns
.102
Exercises
.108
3.3
Voronoi Diagrams
.109
Exercises
.116
3.4
Voronoi Cells in Lattices
.117
Exercises
.124
3.5
Periodic Tilings
.125
Exercises
.133
3.6
All Types of Periodic Tilings
.133
Exercises
.:.144
4
CURVES
.145
4.1
Circles, Powers, and Cyclic Quadrilaterals
.146
Exercises
.161
4.2
Trigonometric Functions and Polar Coordinates
.163
Exercises
.171
4.3
Turning.the Plane Inside Out
.175
Exercises
.183
4.4
Conies
.185
Exercises
.200
4.5
Homogeneous Coordinates and Polarity
.203
Exercises
.222
4.6
The Parametric Equations of a Curve, Cycloids
.225
Exercises
.249
5
SOLID GEOMETRY
.255
5.1
The Basic Assumptions of Solid Geometry
.256
Exercises
.265
5.2
Local Coordinates, the Inner and Outer Products
.266
Exercises
.275
5.3
What Exactly Do I See?
.277
Exercise
.284
5.4
Transformations of Three-Space
.284
Exercises
.297
5.5
Symmetry and Regular Polyhedra
.298
Exercises
.313
5.6
Quadrics and Ruled Surfaces
.314
Exercises
.330
A Basic Assumptions
.333
References
.337
Index
.341 |
| adam_txt |
Contents
1 PLANE
GEOMETRY
. 1
1.1
The Pythagorean Theorem
. 2
Exercises
. 7
1.2
Metrics and Metric Spaces
. 8
Exercises
. 10
1.3
Isometries
. 11
Exercises
. 14
1.4
The Basic Assumptions of Plane Geometry
. 15
Exercises
. 22
1.5
Local Coordinates and the Equation of a Line
. 22
Exercises
. 30
1.6
The Inner Product and Determinant
. 31
Exercises
. 36
2
TRANSFORMATIONS
. 37
2.1
The Reflection in a Line, Congruence
. 38
Exercises
. 44
2.2
Angle Measure, Orientation
. 45
Exercises
. 53
2.3
The Reflection in a Point
. 53
Exercises
. 60
2.4
Translation and Rotation Groups
. 61
Exercises
. 75
2.5
Dilation and Similarity
. 76
Exercises
. 84
2.6
Fractals, Dimension, and Measure
. 86
Exercises
. 93
3
SYMMETRY
. 95
3.1
What Is Symmetry?
. 96
Exercises
. 101
xiv Contents
3.2
There Are Seven Types of Frieze Patterns
.102
Exercises
.108
3.3
Voronoi Diagrams
.109
Exercises
.116
3.4
Voronoi Cells in Lattices
.117
Exercises
.124
3.5
Periodic Tilings
.125
Exercises
.133
3.6
All Types of Periodic Tilings
.133
Exercises
.:.144
4
CURVES
.145
4.1
Circles, Powers, and Cyclic Quadrilaterals
.146
Exercises
.161
4.2
Trigonometric Functions and Polar Coordinates
.163
Exercises
.171
4.3
Turning.the Plane Inside Out
.175
Exercises
.183
4.4
Conies
.185
Exercises
.200
4.5
Homogeneous Coordinates and Polarity
.203
Exercises
.222
4.6
The Parametric Equations of a Curve, Cycloids
.225
Exercises
.249
5
SOLID GEOMETRY
.255
5.1
The Basic Assumptions of Solid Geometry
.256
Exercises
.265
5.2
Local Coordinates, the Inner and Outer Products
.266
Exercises
.275
5.3
What Exactly Do I See?
.277
Exercise
.284
5.4
Transformations of Three-Space
.284
Exercises
.297
5.5
Symmetry and Regular Polyhedra
.298
Exercises
.313
5.6
Quadrics and Ruled Surfaces
.314
Exercises
.330
A Basic Assumptions
.333
References
.337
Index
.341 |
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| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| language | English Dutch |
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| spelling | Aarts, J. M. 1938-2018 Verfasser (DE-588)1077023162 aut Meetkunde Plane and solid geometry J. M. Aarts New York, NY Springer 2008 XIV, 349 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Aus dem Niederländ. übers. "The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry as well as tools for other subjects."--Back cover Geometry, Plane Geometry, Solid Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Euklidische Geometrie (DE-588)4137555-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3061999&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754376&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4137555-5 (DE-588)4123623-3 |
| title | Plane and solid geometry |
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| title_auth | Plane and solid geometry |
| title_exact_search | Plane and solid geometry |
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| title_fullStr | Plane and solid geometry J. M. Aarts |
| title_full_unstemmed | Plane and solid geometry J. M. Aarts |
| title_short | Plane and solid geometry |
| title_sort | plane and solid geometry |
| topic | Geometry, Plane Geometry, Solid Euklidische Geometrie (DE-588)4137555-5 gnd |
| topic_facet | Geometry, Plane Geometry, Solid Euklidische Geometrie Lehrbuch |
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