Numbers and geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1998
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 339 S. zahlr. graph. Darst. |
| ISBN: | 0387982892 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Arithmetic 1
1.1 The Natural Numbers 1
1.2 Division, Divisors, and Primes 4
1.3 The Mysterious Sequence of Primes 7
1.4 Integers and Rationals 9
1.5 Linear Equations 13
1.6 Unique Prime Factorization 17
1.7 Prime Factorization and Divisors 20
1.8 Induction 23
1.9* Foundations 26
1.10 Discussion 30
2 Geometry 37
2.1 Geometric Intuition 37
2.2 Constructions 40
2.3 Parallels and Angles 44
2.4 Angles and Circles 47
2.5 Length and Area 50
2.6 The Pythagorean Theorem 53
xi
2.7 Volume 56
2.8* The Whole and the Part 59
2.9 Discussion 64
3 Coordinates 69
3.1 Lines and Circles 69
3.2 Intersections 72
3.3 The Real Numbers 77
3.4 The Line 82
3.5 The Euclidean Plane 85
3.6 Isometries of the Euclidean Plane 89
3.7 The Triangle Inequality 93
3.8* Klein s Definition of Geometry 95
3.9* The Non Euclidean Plane 100
3.10 Discussion 105
4 Rational Points 111
4.1 Pythagorean Triples Ill
4.2 Pythagorean Triples in Euclid 113
4.3 Pythagorean Triples in Diophantus 116
4.4 Rational Triangles 120
4.5 Rational Points on Quadratic Curves 124
4.6* Rational Points on the Sphere 127
4.7* The Area of Rational Right Triangles 131
4.8 Discussion 136
5 Trigonometry 143
5.1 Angle Measure 143
5.2 Circular Functions 147
5.3 Addition Formulas 152
5.4 A Rational Addition Formula 156
5.5* Hilbert s Third Problem 159
5.6* The Dehn Invariant 161
5.7* Additive Functions 165
5.8* The Tetrahedron and the Cube 168
5.9 Discussion 171
6 Finite Arithmetic 177
6.1 Three Examples 177
6.2 Arithmetic mod n 179
6.3 The Ring Z/nZ 183
6.4 Inverses mod n 186
6.5 The Theorems of Fermat and Wilson 190
6.6 The Chinese Remainder Theorem 194
6.7 Squares mod p 197
6.8* The Quadratic Character of 1 and 2 200
6.9* Quadratic Reciprocity 203
6.10 Discussion 208
7 Complex Numbers 215
7.1 Addition, Multiplication, and Absolute Value 215
7.2 Argument and the Square Root of—1 219
7.3 Isometries of the Plane 223
7.4 The Gaussian Integers 227
7.5 Unique Gaussian Prime Factorization 230
7.6 Fermat s Two Squares Theorem 233
7.7* Factorizing a Sum of Two Squares 237
7.8 Discussion 238
8 Conic Sections 247
8.1 Too Much, Too Little, and Just Right 247
8.2 Properties of Conic Sections 251
8.3 Quadratic Curves 255
8.4* Intersections 260
8.5 Integer Points on Conies 263
8.6* Square Roots and the Euclidean Algorithm 267
8.7* Pell s Equation 271
8.8 Discussion 275
9 Elementary Functions 281
9.1 Algebraic and Transcendental Functions 281
9.2 The Area Bounded by a Curve 284
9.3 The Natural Logarithm and the Exponential 287
9.4 The Exponential Function 292
9.5 The Hyperbolic Functions 295
9.6 The Pell Equation Revisited 298
9.7 Discussion 303
Bibliography 311
Index 317
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 0387982892 |
| language | English |
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| spelling | Stillwell, John 1942- Verfasser (DE-588)128427264 aut Numbers and geometry John Stillwell New York [u.a.] Springer 1998 XIV, 339 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Geometrie - Lehrbuch Zahlentheorie - Lehrbuch Mathematik Mathematics Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Geometrie (DE-588)4020236-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007933859&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stillwell, John 1942- Numbers and geometry Geometrie - Lehrbuch Zahlentheorie - Lehrbuch Mathematik Mathematics Zahlentheorie (DE-588)4067277-3 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4020236-7 (DE-588)4123623-3 |
| title | Numbers and geometry |
| title_auth | Numbers and geometry |
| title_exact_search | Numbers and geometry |
| title_full | Numbers and geometry John Stillwell |
| title_fullStr | Numbers and geometry John Stillwell |
| title_full_unstemmed | Numbers and geometry John Stillwell |
| title_short | Numbers and geometry |
| title_sort | numbers and geometry |
| topic | Geometrie - Lehrbuch Zahlentheorie - Lehrbuch Mathematik Mathematics Zahlentheorie (DE-588)4067277-3 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometrie - Lehrbuch Zahlentheorie - Lehrbuch Mathematik Mathematics Zahlentheorie Geometrie Lehrbuch |
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