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Download Episodes in the Mathematics of Medieval Islam by J.L. Berggren PDF

By J.L. Berggren

This e-book offers episodes from the math of medieval Islam, paintings which has had an outstanding impression at the improvement of arithmetic. the writer describes the topic in its right historic context, bearing on particular Arabic texts. one of the subject matters mentioned are decimal mathematics, airplane and round trigonometry, algebra, interpolation and approximation of roots of equations. This booklet will be of significant curiosity to historians of arithmetic, in addition to to scholars of arithmetic. The presentation is quickly available to someone with a historical past in highschool mathematics.

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Sample text

The Decimal System Muslim mathematicians were the first people to write numbers the way we do, and, although we are the heirs of the Greeks in geometry, part of our legacy from the Muslim world is our arithmetic. This is true even if it was Hindu mathematicians in India, probably a few centuries before the rise of Islamic civilization, who began using a numeration system with these two characteristics: 1. The numbers from one to nine are represented by nine digits, all easily made by one or two strokes.

The examples of what was written on the dust board, however, may have been viewed as illustrations, much like a diagram in a geometrical argument, and they were there to show what the calculator would actually see on the dust board. Addition As Kiishyar explains this, the numbers to be added are written in two rows, one above the other, so that places of the same value are in the same column. He gives the example of adding 839 to 5625 and, unlike our method, begins his addition by adding from the highest place common to both numbers, in this case the hundreds' place, down.

First, he expresses both factors in terms of their lowest orders, Thus: 4°15' = (4·60)' + 15' = 235', and 235'20" = (235·60)" + 20" = 14,120". Similarly, he calculates the other factor to be 22,813". Since the books that discuss this method explain how to calculate the products of various orders, al-NasawI knows that the product of "seconds" by "seconds" will be on the order of "fourths" and, calculating in pure decimal numbers, he finds the product to be 322,119,560 fourths. Now it is necessary to perform the inverse operation of levelling, namely to "raise" this number to a sexagesimal expression, by dividing by 60.

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