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

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The improvement of computing has reawakened curiosity in algorithms. frequently overlooked by means of historians and glossy scientists, algorithmic techniques were instrumental within the improvement of primary rules: perform resulted in idea simply up to the opposite direction around. the aim of this e-book is to provide a ancient heritage to modern algorithmic perform.

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Additional info for A History of Algorithms: From the Pebble to the Microchip

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114-117). The calculation technique uses the fact that numbers are written using positional notation. 4 Tableau Multiplication 21 ten down and arranged in a geometrical configuration which provides for the different decimal or sexagesimal positions. 3 5 To take an example, consider one found in the 16th ceritury Indian astronomer Ganesa's commentary on the 12th century Indian book Liliivati by Bhaskara [5]. The results of the 2 o 6 separate products for the multiplication of l35 by 12 appear in the small squares.

The scribe writes the 'numerators' in red. Thus: = = = = 1/4 7/28 1/8 (3 + 112)/28 1128 = 1128 1/56 = (112)128 1116 (1 + 112 + 1/4)/28 1/112 (114)128 The sum of the 'numerators' is equal to: (7 + 1) + (3 + 112 + 1/2) + (1 + 1/2 + 114 + 1/4). This can be done easily since, the scribe proceeding by mediation, it is made up only of integers or unit fractions with denominators which are powers of 2. We immediately find that the sum is 14, which is half of 28, and the total is therefore 112. The scribe uses 28 as the 'common denominator' since it appears as part of the data of the problem, even though the mediation process will end up with non integer 'numerators'.

He made several practical advances in this direction in 1673 and, some thirty years after Pascal's adding machine, he invented a machine for the four operations of arithmetic. He also invented. in 1674. a machine capable of solving equations and even envisaged a type of cylinder that could be used to produce theorems. With the birth of 44 1 Algorithms for Arithmetic Operations the computer, Leibniz's dream has been, to a certain extent, realised today. The modern computer was preceded by many other calculating machines, like Babbage's 'difference engine' in 1822 (see Chapter 10), and the inventions by Bouchon, Falcon and Jacquard for automating the weaving of fabrics.

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