By Karl Menninger
'The historian of arithmetic will locate a lot to curiosity him the following . . . whereas the informal reader might be intrigued through the author's enhanced narrative ability." — Library Journal
This e-book is not just a desirable creation to the concept that of quantity and to numbers themselves, hut a multifaceted linguistic and historic research of the way numbers have constructed and advanced in lots of varied cultures. Drawing on proof from heritage, literature, philosophy and ethnology, famous German pupil Karl Menninger. recounts the improvement of numbers either as they're spoken (and written as phrases) and as symbolic summary numerals which could he without problems manipulated and combined.
Despite the gigantic erudition the writer brings to the subject, he continues a mild tone all through, providing a lot of the knowledge in anecdotal shape. in addition, nearly three hundred illustrations (photographs and drawings) and lots of comparative language tables serve to reinforce the textual content. the writer starts with a lucid therapy of quantity series and quantity language, together with the formation of quantity phrases in either Indo-European and non-IndoEuropean languages, hidden quantity phrases and the evolution of the quantity series. He then turns to written numerals and computations: finger counting, folks symbols for numbers, alphabetical numerals, the "German" Roman numerals, the abacus and extra. the ultimate part matters the advance of our modem decimal procedure, with its position notation and nil, in line with the Indian quantity method, and its advent to the West in the course of the paintings of the Italian mathematician Fibonacci. the writer concludes with a assessment of spoken numbers and quantity symbols in China and Japan.
"The ebook is principally solid on early counting and calculating units: primitive tally sticks, the knotted cords of historical Peru, the frilly finger symbols as soon as used for numbers, counting forums with movable counters, and naturally the abacus." — Martin Gardner, Book World
Quick preview of Number Words and Number Symbols: A Cultural History of Numbers PDF
All of the tables has 3 varied counting components, with coin rows, that are divided into components at the later desk, proven lower than. traces and coinage symbols are inlaid in different-colored wooden (d for pence, s for shillings, lb and lib for kilos and X, C, and M pounds). The counters have been saved in drawers. The reduce reckoning desk has a raised aspect to maintain the counters from by chance falling off. The tables are a hundred thirty × ninety eight cm and 209 × eighty five cm in dimension, respectively, with the marked components seventy five × forty five cm at the top and sixty two × forty three at the reduce desk.
Multiplicationes in manibus addiscendo semper ulantur colligere, ut animus pariter cum manibus in additionibus et multiplicationibus quorum-libet numerorum expeditior fiat, … multiplication with the palms has to be practiced continually, in order that the brain just like the arms turns into more proficient at including and multiplying a number of numbers. (Compare the passage quoted from St. Augustine, p. 210). different medieval and early glossy writers, despite the fact that, even though they wrote approximately finger counting, say not anything approximately computations utilizing the arms; probably they weren't too usually used.
Three cm. Ethnographic Museum, Munich. Fig. 245 an identical seal as Fig. 244. nine. five cm excessive. Fig. 246 street marker indicating the eightieth kilometer alongside the Aleppo-Latakia street. photo by means of U. Dubs. Fig. 247 Entries within the Regensburg Annals. 726 Charles (the nice) made struggle at the Saracens (Arabs) . . . 727 . . . 731 Bede the Priest died [the related Venerable Bede whose finger gestures we've got already obvious a lot previous, see p. 201] … 732 … 734 . . . 737 Charles made conflict at the Saxons 744 Charles died and used to be buried in Paris Fig.
Therefore the single old Egyptian non-unit fraction 2/3 used to be referred to as “both parts”; an analogous fraction in Akkadian-Babylonian used to be termed “both arms. ” The curious Roman identify bes for aes can also be defined during this demeanour: Latin bes < duessis < duo (partes) assis, “2 (parts) of the aes. ” glossy Greek says for , , and tà dýo (tría, téssera) mérē, “the (three, 4) components. ” previous Norse then has a strange demeanour of expressing a fragment whose denominator is greater than the numerator by means of greater than 1 half: “ (of the fish stuck within the River Grima belong to the Church)” is fim hluter en þri huerta undan, five components and three cross beneath.
English translation copyright © 1969 by means of The Massachusetts Institute of expertise. All rights reserved. This Dover variation, first released in 1992, is an unabridged, unaltered republication of the English translation (published through The MIT Press, Cambridge, Mass. , 1969) of the revised German version of Zahlwort und Ziffer: Eine Kulturgeschichte der Zahlen, released by way of the Vandenhoeck & Ruprecht Publishing corporation, Göttingen, Germany, 1957–58. The Dover version is released by means of specified association with Vandenhoeck & Ruprecht GmbH & Co.