From one to zero: a universal history of numbers
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
New York, N.Y. u.a.
Viking
1985
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI,503 S. zahlr. Ill. |
| ISBN: | 0670373958 |
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Datensatz im Suchindex
| _version_ | 1804133324438896640 |
|---|---|
| adam_text | Contents
Introduction xi
/. AWARENESS OF NUMBERS 1
1 The Origin and Discovery of Numbers 3
Are animals able to count? 3
Natural faculties of number perception 5
Can one define a quantity without knowing how to count? 8
Rudimentary accounting techniques 14
Expressing number orally and by gestures 15
Counting: a human faculty 21
Symbolization of number 25
Ten fingers for counting 26
2 The Principle of the Base 31
Decimal systems 31
Traces of the base 5 36
Twenty fingers and toes for counting 38
The sexagesimal system 46
The origin of the sexagesimal system 49
//. CONCRETE COUNTING 53
3 The First Calculating Machine: The Hand 55
A curious way of bargaining 59
Counting on the bones and joints of the fingers 61
Morra, a finger game 67
Elements of finger computation 70
An elaborate system of finger counting 72
History recounted on the fingers 76
nun
I——, Contents
4 Notching 81
5 From Pebbles to Calculation 88
6 Numbers on Strings 91
The archives of the Incas 91
Use of knotted strings in other parts of the world 94
7 Number, Value, Money 98
8 The Abacus 105
Greek and Roman abacuses 105
The first pocket calculator 111
Abacists versus algorists: the Renaissance 113
Rods on the Chinese counting board 117
The bead abacus 121
///. THE INVENTION OF NUMERALS 129
9 Roman Numerals: A Vestige of Primitive Origins? 131
The numerals of Roman civilization 131
Questionable ancestors 134
The origin of Roman numerals 136
Anthropological and historical evidence 143
10 Was Writing Invented by Accountants? 151
Five thousand years ago, the Sumerians and Elamites
learned to write 151
Precursors of written accounting 154
From clay envelopes to account tablets 155
The mnemonic function of Sumerian writing 165
11 Sumerian Numerals 170
The development of cuneiform numerals 173
Difficulties of the cuneiform numeration system 177
Continuance of the Sumerian system 179
How modern scholars deciphered Sumerian numerals 180
12 Deciphering a Forgotten Notation 182
13 Egyptian Numerals 200
The origin of hieroglyphs: Sumerian or Egyptian? 202
From drawings to numerals 203
Fractions and the dismembered god 207
Contents ; . i
14 Kindred Numeration Systems 213
Cretan numerals 213
The Hittite hieroglyphic system 218
The Aztec system 219
Greek acrophonic systems 225
Numerals of the Kingdom of Saba 229
A significant improvement 233
15 The Egyptian Scribes Rapid Notation 240
Hieratic script 241
A remarkable simplification 244
Numerals in the time of the Hebrew kings 246
IV. NUMERALS AND LETTERS 249
16 Numerical Use of the Hebrew Alphabet 251
17 Greek Alphabetic Numerals 261
18 The Phoenician Origin of Numeral Letters: A Legend 275
19 Syriac Numerals 279
20 Arabic Numeral Letters 282
21 Numerals, Letters, Magic, Mysticism, and Divination 291
The art and composition of chronograms 291
Interpretations and speculations of Gnostics, Cabalists,
magicians, and soothsayers 293
V. HYBRID NUMERATION SYSTEMS 311
22 The Drawbacks of the Additive Principle 313
Roman notations for large numbers 313
Appearance and extension of the multiplicative principle 320
23 The Common Mesopotamian Numeration System 325
24 Semitic Numerical Traditions 332
25 The Traditional Chinese Numeration System 341
The modern system 341
Different forms of Chinese numerals 343
. , Contents
Origin of the Chinese system 347
Diffusion of the Chinese system in the Far East 353
Systems similar to the common Chinese system 356
A natural extension 361
Chinese notations of large numbers in scientific works 365
VI. THE ULTIMATE STAGE OF NUMERICAL NOTATION 369
26 The First Place Value Numeration System 371
The Babylonian place value system 373
Difficulties of this system 375
The oldest zero in history 376
Survival of the Babylonian system 382
27 The Chinese Place Value System 387
28 Amazing Achievements of a Vanished Civilization 397
Greatness and decline of Mayan civilization 397
Sources of our knowledge 398
Six centuries of intellectual and artistic achievement 400
Writing, arithmetic, and astronomy 403
The Mayan calendar 405
Chronology and numeration 412
Discovery of the place value principle and the zero in the
New World 420
Conclusion 426
29 The Origin of Hindu Arabic Numerals 428
The keystone of our modern numeration system 428
A significant anecdote 434
The cradle of our modern system 437
The symbolic number words of Indian astronomers 445
Origin of the Indian place value system 452
Worldwide propagation of the Indian system 459
Adoption of the Indian system by the Eastern Arabs 462
Numerals used by the Western Arabs 473
Hindu Arabic numerals in Europe 475
Chronology 491
Bibliography of Works Quoted or Mentioned in This Book 499
Acknowledgments 503
|
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| id | DE-604.BV019821604 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:54Z |
| institution | BVB |
| isbn | 0670373958 |
| language | English French |
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| physical | XVI,503 S. zahlr. Ill. |
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| spelling | Ifrah, Georges 1947- Verfasser (DE-588)103559760 aut Histoire universelle des chiffres From one to zero a universal history of numbers Georges Ifrah. Lowell Bair [Übers.] New York, N.Y. u.a. Viking 1985 XVI,503 S. zahlr. Ill. txt rdacontent n rdamedia nc rdacarrier Geschichte gnd rswk-swf Geschichte Numerals History Numeration History Ziffer (DE-588)4190809-0 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Zahlensystem (DE-588)4117700-9 gnd rswk-swf Computer (DE-588)4070083-5 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Zahl (DE-588)4067271-2 gnd rswk-swf Zahl (DE-588)4067271-2 s Geschichte (DE-588)4020517-4 s DE-604 Ziffer (DE-588)4190809-0 s Zahlensystem (DE-588)4117700-9 s Geschichte z 1\p DE-604 Datenverarbeitung (DE-588)4011152-0 s 2\p DE-604 Computer (DE-588)4070083-5 s 3\p DE-604 Bair, Lowell trl HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013146865&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ifrah, Georges 1947- From one to zero a universal history of numbers Geschichte Numerals History Numeration History Ziffer (DE-588)4190809-0 gnd Datenverarbeitung (DE-588)4011152-0 gnd Zahlensystem (DE-588)4117700-9 gnd Computer (DE-588)4070083-5 gnd Geschichte (DE-588)4020517-4 gnd Zahl (DE-588)4067271-2 gnd |
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| title | From one to zero a universal history of numbers |
| title_alt | Histoire universelle des chiffres |
| title_auth | From one to zero a universal history of numbers |
| title_exact_search | From one to zero a universal history of numbers |
| title_full | From one to zero a universal history of numbers Georges Ifrah. Lowell Bair [Übers.] |
| title_fullStr | From one to zero a universal history of numbers Georges Ifrah. Lowell Bair [Übers.] |
| title_full_unstemmed | From one to zero a universal history of numbers Georges Ifrah. Lowell Bair [Übers.] |
| title_short | From one to zero |
| title_sort | from one to zero a universal history of numbers |
| title_sub | a universal history of numbers |
| topic | Geschichte Numerals History Numeration History Ziffer (DE-588)4190809-0 gnd Datenverarbeitung (DE-588)4011152-0 gnd Zahlensystem (DE-588)4117700-9 gnd Computer (DE-588)4070083-5 gnd Geschichte (DE-588)4020517-4 gnd Zahl (DE-588)4067271-2 gnd |
| topic_facet | Geschichte Numerals History Numeration History Ziffer Datenverarbeitung Zahlensystem Computer Zahl |
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