Number Words and Number Symbols (eBook)

Karl Menninger (Autor)

eBook Download: EPUB

2013
512 Seiten
Dover Publications (Verlag)
978-0-486-31977-3 (ISBN)

Infos

Classic study discusses number sequence and number language, then explores written numerals and computations in a wide range of cultures. 282 illustrations. "Superior narrative ability." — Library Journal.

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''The historian of mathematics will find much to interest him here . . . while the casual reader is likely to be intrigued by the author's superior narrative ability."e; — Library JournalThis book is not only a fascinating introduction to the concept of number and to numbers themselves, hut a multifaceted linguistic and historical analysis of how numbers have developed and evolved in many different cultures. Drawing on evidence from history, literature, philosophy and ethnology, noted German scholar Karl Menninger. recounts the development of numbers both as they are spoken (and written as words) and as symbolic abstract numerals that can he readily manipulated and combined.Despite the immense erudition the author brings to the topic, he maintains a light tone throughout, presenting much of the information in anecdotal form. Moreover, almost 300 illustrations (photographs and drawings) and many comparative language tables serve to enhance the text. The author begins with a lucid treatment of number sequence and number language, including the formation of number words in both Indo-European and non-IndoEuropean languages, hidden number words and the evolution of the number sequence. He then turns to written numerals and computations: finger counting, folk symbols for numbers, alphabetical numerals, the "e;German"e; Roman numerals, the abacus and more. The final section concerns the development of our modem decimal system, with its place notation and zero, based on the Indian number system, and its introduction to the West through the work of the Italian mathematician Fibonacci. The author concludes with a review of spoken numbers and number symbols in China and Japan."e;The book is especially good on early counting and calculating devices: primitive tally sticks, the knotted cords of ancient Peru, the elaborate finger symbols once used for numbers, counting boards with movable counters, and of course the abacus."e; — Martin Gardner, Book World

Inhalt

PrefaceList of Phonetic SymbolsNUMBER SEQUENCE AND NUMBER LANGUAGEIntroductionThe Number Sequence The Abstract Number Sequence The Number Sequence Use Concretely NUMBERS WITHOUT WORDS NUMBERS AS ATTRIBUTES NUMBERS AS ADJECTIVES Expansion of the Number Sequence by Means of Supplementary Quantities NUMBERING BY FINGERS AND TOES Principles of the Number Sequence SUCCESSION AND GROUP GROUPINGS OF HIGHER RANK GRADATION BY STEPS GROUPINGS IN THE GRADUATED NUMBER SEQUENCE "20-GROUP "MAN" NUMBER LANGUAGE AND NUMBER SYMBOLS Historical Gradations REPRESENTING THE GRADATION NUMBER SYSTEMS BASED ON GRADATIONS OF 20 VIGESIMAL GRADATIONS IN EUROPEAN NUMBER SEQUENCES THE AINU NUMBER SEQUENCE Laws Governing the Formation of Number Words SUCCESSION OF MAGNITUDES BACK-COUNTING OVERCOUNTING ADDITIONAL WAYS OF FORMING NUMBER WORDS THE FIRST STEPS BEYOND TENOur Number Words Indo-European Family Languages SURVEY OF LANGUAGES AND NUMBER WORDS THE ORIGINAL INDO-EUROPEAN LANGUAGE THE INDIVIDUAL INDO-EUROPEAN LANGUAGES The Non-Indo-European Languages The Meaning of Our Number Words IMAGES BEHIND THE CONCEPTS OF SIZE AND NUMBER SEMANTIC FADING OUR INDO-EUROPEAN NUMBER WORDS Was There a Babylonian Influence on Our Number Sequence? THE BREAK AFTER SIXTY THE ROLE PLAYED BY THE NUMBER SIXTY IN CULTURAL HISTORY GREAT HUNDRED THE NUMBER TWELVE AS THE BASIC UNIT OF THE GREAT HUNDRED THE ROMAN DUODECIMAL FRACTIONS THE BABYLONIAN SEXAGESIMAL SYSTEM THE BREAK AFTER SIXTY IN THE GERMANIC NUMBER SEQUENCE Hidden Number Words ONE TWO THREE FOUR FIVE SIX SEVEN NINE TEN TWENTY FORTY FIFTY SEVENTY HUNDRED THOUSAND NUMBER The Evolution of the Number Sequence FOREIGN LOAN WORDSWRITTEN NUMERALS AND COMPUTATIONSPrefaceIntroductionFinger Counting Finger Counting THE VENERABLE BEDE AND HIS FINGER COUNTING FINGER COUNTING IN ANTIQUITY FINGER COUNTING IN ARABIC AND EAST AFRICAN COMMERCE TRADE ROMAN FINGER COUNTING IN THE WEST COMPUTATIONS ON THE FINGERS SOME FORMS OF FINGER COUNTING USE BY PEOPLES OF OTHER CULTURESFolk Symbols for Numbers Tally Sticks EARLY WRITING AND READING TALLY STICKS WERE UNIVERSAL VARIETIES OF TALLY STICKS THE BRITISH EXCHEQUER TALLIES THE NUMBERS ON THE TALLY STICKS ROMAN NUMERALS CHINESE HAN STICKS Peasant Numerals Knots Used as NumeralsAlphabetical Numerals The Gothic Numerals Letters and Numbers HISTORY OF THE ALPHABET The Two Greek Sets of Numerals Some Other Connections Between Letters and Numbers"The "German" Roman Numerals" Roman Numerals in Cursive Form MEDIEVAL NUMBERS THE GRADUAL PENETRATION OF THE NEW INDIAN NUMERALS THE ACCOUNT BOOKS OF THE IMPERIAL FREE CITY OF AUGSBURG WRITTEN NUMERALS AND COMPUTATIONSThe Abacus The Nature of the Counting Board The Counting Board in Ancient Civilizations THE SALAMIS TABLET DARIUS VASE THE ETRUSCAN CAMEO THE ROMAN HAND ABACUS THE HAND ABACUS IN ASIA THE ROMAN COUNTING BOARD WITH LOOSE COUNTERS The Counting Board in the Early Middle Ages THE WEST THE MONASTIC ABACUS The Counting Board in the Later Middle Ages THE EVIDENCE FOR ITS USE THE NEW RECKONING BOARD THE NAMES OF THE COUNTING BOARDS "RECKONING "ON THE LINES" THE COUNTING BOARD IN EVERYDAY LIFE THE COUNTING BOARD AND WRITTEN NUMERALS The CountersOur Own Numerals Place-Value Notation The Antecedents of Our Numerals THE KHAROSTHI NUMERALS THE BRAHMI NUMERALS PLACE-VALUE NOTATION The Westward Migration of the Indian Numerals THE ZERO ALEXANDRIA THE INDIAN NUMERALS IN ARAB HANDS THE FAMILY TREE OF INDIAN NUMERALS The Indian Numerals in Western Europe ITALY LEONARDO OF PISA THE GERMAN ARITHMETICIANS "THE "NEW" NUMERALS" RETROSPECTSpoken Numbers and Number Symbols in China and Japan Far Eastern Number Systems Spoken Numbers THE CHINESE NUMBER WORDS JAPANESE NUMBER WORDS KOREAN NUMBER WORDS SUMMARY WRITTEN NUMERALS RETROSPECT: SPOKEN LANGUAGE?WRITING?WRITTEN NUMERALSIndex

Produkt-Details

• Erscheint lt. Verlag: 10.4.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-486-31977-6 / 0486319776
• ISBN-13: 978-0-486-31977-3 / 9780486319773