Geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2001
|
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 313 S. Illustrationen |
| ISBN: | 1852330589 |
Staff View
MARC
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| 100 | 1 | |a Fenn, Roger |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry |c Roger Fenn |
| 264 | 1 | |a London [u.a.] |b Springer |c 2001 | |
| 300 | |a XII, 313 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer undergraduate mathematics series | |
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Record in the Search Index
| _version_ | 1816443617671118848 |
|---|---|
| adam_text |
CONTENTS
1.
THE
GEOMETRY
OF
NUMBERS
.
1
1.1
NATURAL
NUMBERS
.
2
1.2
ADDING
NATURAL
NUMBERS
.
4
1.3
MULTIPLYING
NATURAL
NUMBERS
.
4
1.4
SQUARE
AND
TRIANGULAR
NUMBERS
.
5
1.5
POWERS
.
9
1.6
ZERO
AND
NEGATIVE
NUMBERS
.
9
1.7
RATIONAL
NUMBERS
OR
FRACTIONS
.
10
1.8
POWERS
OF
RATIONAL
NUMBERS
.
14
1.9
RATIONAL
NUMBERS
AS
A
FIELD
.
14
1.10
REAL
NUMBERS
.
15
1.11
IRRATIONAL
NUMBERS
.
16
1.12
FOUR
FAMOUS
NUMBERS:
Y/2,
VR,
T
,
E
.
16
2.
COORDINATE
GEOMETRY
.
29
2.1
COORDINATES
.
29
2.2
R
N
,
THE
SPACE
OF
COORDINATES
.
30
2.3
THE
LINE
THROUGH
TWO
POINTS
.
35
2.4
THE
PLANE
CONTAINING
THREE
POINTS
.
36
2.5
DISTANCE
AND
ANGLE
.
38
2.6
POLAR
COORDINATES
.
44
2.7
AREA
.
48
2.8
HYPERPLANES
.
51
2.9
ANGLES
BETWEEN
HYPERPLANES
AND
NEAREST
POINTS
TO
HYPERPLANES
55
X
CONTENTS
3.
THE
GEOMETRY
OF
THE
EUCLIDEAN
PLANE
.
63
3.1
THE
LIFE
OF
EUCLID
.
63
3.2
THE
EUCLIDEAN
AXIOMS
FOR
THE
PLANE
.
64
3.3
ANGLES
AND
LINES
.
65
3.4
SOME
BASIC
FACTS
ABOUT
TRIANGLES
.
67
3.5
GENERAL
POLYGONS
.
69
3.6
CONGRUENCES
AND
SIMILARITIES
.
73
3.7
ISOSCELES
TRIANGLES
.
76
3.8
CIRCLES
.
78
3.9
TRIANGLES
AND
THEIR
CENTRES
.
83
3.10
METRIC
PROPERTIES
OF
TRIANGLES
.
87
3.11
THREE
SURPRISING
(AND
BEAUTIFUL)
THEOREMS
.
89
4.
THE
GEOMETRY
OF
COMPLEX
NUMBERS
.
99
4.1
WHAT
IS
\Z-1
?
.
100
4.2
MODULUS
AND
DIVISION
.
103
4.3
UNIMODULAR
COMPLEX
NUMBERS
AND
THE
UNIT
CIRCLE
.
104
4.4
LINES
AND
CIRCLES
IN
THE
COMPLEX
PLANE
.
106
4.5
MANIPULATING
COMPLEX
NUMBERS
.
107
4.6
INFINITY
AND
THE
RIEMANN
SPHERE
.
ILL
4.7
DIVISION
AND
INVERSION
.
115
4.8
MOBIUS
TRANSFORMATIONS
.
118
4.9
CROSS
RATIOS
.
120
4.10
A
FORMULA
FOR
THE
CROSS
RATIO
.
125
4.11
ROOTS
OF
UNITY
.
127
4.12
FORMULAE
FOR
THE
NTH
ROOTS
OF
UNITY
.
127
4.13
SOLVING
CUBIC
AND
BIQUADRATIC
POLYNOMIALS
.
130
5.
SOLID
GEOMETRY
.
137
5.1
POINTS
AND
COORDINATES
.
137
5.2
SCALAR
PRODUCT
.
141
5.3
CROSS
PRODUCT
.
142
5.4
THE
SCALAR
TRIPLE
PRODUCT
.
144
5.5
THE
VECTOR
TRIPLE
PRODUCT
.
146
5.6
PLANES
.
147
5.7
LINES
IN
SPACE
.
149
5.8
ISOMETRIES
OF
SPACE
.
154
5.9
PROJECTIONS
.
162
5.10
POLYHEDRA
.
166
CONTENTS
XI
6.
PROJECTIVE
GEOMETRY
.
183
6.1
THE
PROJECTIVE
PLANE
.
184
6.2
LINES
IN
THE
PROJECTIVE
PLANE
.
185
6.3
INCIDENCE
AND
DUALITY
.
186
6.4
DESARGUES
'
THEOREM
.
188
6.5
CROSS
RATIOS
AGAIN
.
190
6.6
CROSS
RATIOS
AND
DUALITY
.
193
6.7
PROJECTIVITIES
AND
PERSPECTIVITIES
.
195
6.8
QUADRILATERALS
.
199
6.9
PROJECTIVE
TRANSFORMATIONS
.
200
6.10
FIXED
POINTS
AND
EIGENVECTORS
.
202
6.11
PAPPUS
'
THEOREM
.
202
6.12
PERSPECTIVE
DRAWING:
TRICKS
OF
THE
TRADE
.
204
6.13
THE
FANO
PLANE
.
207
7.
CONICS
AND
QUADRIC
SURFACES
.
211
7.1
CONIC
SECTIONS
.
212
7.2
THE
CONIC
AS
QUADRATIC
CURVE
.
214
7.3
FOCAL
PROPERTIES
OF
CONICS
.
225
7.4
THE
MOTION
OF
THE
PLANETS
.
231
7.5
QUADRIC
SURFACES
.
238
7.6
THE
GENERA]
QUADRIC
SURFACE
.
244
8.
SPHERICAL
GEOMETRY
.
253
8.1
GEODESICS
.
255
8.2
GEODESIC
TRIANGLES
.
256
8.3
LATITUDE
AND
LONGITUDE
.
260
8.4
COMPASS
BEARINGS
.
264
8.5
THE
CELESTIAL
SPHERE
.
269
8.6
OBSERVER
'
S
COORDINATES
.
272
8.7
TIME
AND
RIGHT
ASCENSION
.
274
9.
QUATERNIONS
AND
OCTONIONS
.
287
9.1
EXTENDED
COMPLEX
NUMBERS
.
287
9.2
MULTIPLYING
QUATERNIONS
.
288
9.3
INVERSES
OF
QUATERNIONS
.
289
9.4
REAL
AND
PURE
PARTS
OF
QUATERNIONS
.
291
9.5
MULTIPLYING
QUATERNIONS
AND
LINEAR
TRANSFORMATIONS
OF
K
4
.
292
9.6
OCTONIONS
.
295
9.7
VECTOR
PRODUCTS
IN
K
7
.
297
9.8
OCTONIONS
AND
ASSOCIATIVITY
.
299
9.9
HEXADECANIONS?
.
300
XII
CONTENTS
BIBLIOGRAPHY
.
305
INDEX
.
307 |
| any_adam_object | 1 |
| author | Fenn, Roger |
| author_facet | Fenn, Roger |
| author_role | aut |
| author_sort | Fenn, Roger |
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| classification_tum | MAT 500f |
| ctrlnum | (OCoLC)44173072 (DE-599)BVBBV013325265 |
| 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 |
| format | Book |
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| id | DE-604.BV013325265 |
| illustrated | Illustrated |
| indexdate | 2024-11-22T17:13:44Z |
| institution | BVB |
| isbn | 1852330589 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009087580 |
| oclc_num | 44173072 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-20 DE-703 DE-91G DE-BY-TUM DE-706 DE-526 DE-634 DE-11 DE-188 |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-20 DE-703 DE-91G DE-BY-TUM DE-706 DE-526 DE-634 DE-11 DE-188 |
| physical | XII, 313 S. Illustrationen |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spelling | Fenn, Roger Verfasser aut Geometry Roger Fenn London [u.a.] Springer 2001 XII, 313 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Geometry Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009087580&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fenn, Roger Geometry Geometry Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 |
| title | Geometry |
| title_auth | Geometry |
| title_exact_search | Geometry |
| title_full | Geometry Roger Fenn |
| title_fullStr | Geometry Roger Fenn |
| title_full_unstemmed | Geometry Roger Fenn |
| title_short | Geometry |
| title_sort | geometry |
| topic | Geometry Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009087580&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fennroger geometry |