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Download A History of Algorithms: From the Pebble to the Microchip by Jean-Luc Chabert, C. Weeks, Evelyne Barbin, J. Borowczyk, M. PDF

By Jean-Luc Chabert, C. Weeks, Evelyne Barbin, J. Borowczyk, M. Guillemot, A. Michel-Pajus, A. Djebbar, Jean-Claude Martzloff

Amazon hyperlink: http://www.amazon.com/History-Algorithms-From-Pebble-Microchip/dp/3540633693

The improvement of computing has reawakened curiosity in algorithms. usually missed through historians and smooth scientists, algorithmic strategies were instrumental within the improvement of basic principles: perform ended in idea simply up to the opposite direction around. the aim of this publication is to supply a old history to modern algorithmic perform.

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C. From Europe As well as in China and the Arab world, the method of multiplication using a tableau is also found in Europe, and has a long history which extends from the Middle Ages right up to the beginning of the twentieth century. The earliest known European example of the use of a tableau appears in a Latin manuscript of about 1300 in England in the reign of Edward II (figure 1). This method is found later in a number of arithmetic books from the Renaissance period, like the Treviso Arithmetic [26], published anonymously in Treviso in 1478 (figure 2) and Luca Pacioli's Suma of 1494 (figure 3).

AI-Hafni, M. , Mifta~ al-~isiib (The Key to Calculation), Cairo, 1967. , Histoire comparee des numerations ecrites, Flammarion, Paris, 1975. G. , A first course in Computer Technology, McGraw-Hill, 1978. , Investigations of an early Sumerial division problem, c. 2500 BC, Historia mathematica 9,1982,19-36. [19] Ibn AI-Majdi,qawi l-lubab (Compendium of the Pith [of Calculations)) Ms. British Museum,n° Add. 7469. , Histoire universelle des chiffres, Seghers, Paris, 1981. , Tablettes sum~riennes de Shuruppak conserv~es au Mus~e de Stamboul, Memoires de l'Institut Franfais d'Archeologie de Stamboul, Boccard, Paris, 1937.

LOn-l, which provides a new dividend on this rank. We shall simulate this algorithm for the example proposed in the text, namely dividing 900 by 8. Our abacus contains three 'vertical' columns, numbered from the left, and four 'horizontal' ranks, numbered from the top down. Initialisation: put the difference (10 - d), here 2, in the first rank of the right hand column. Then place the divisor d, here 8, on the second rank of the same column. Finally, put the dividend on the third rank, with the units digit in the right hand column.

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