Download e-book for iPad: A History of Numerical Analysis from the 16th through the by H. H. Goldstine

By H. H. Goldstine

ISBN-10: 0387902775

ISBN-13: 9780387902777

ISBN-10: 3540902775

ISBN-13: 9783540902775

The beaver's enamel and the tiger's claw. Sunflowers and seashells. Fractals, Fibonacci sequences, logarithmic spirals. those assorted varieties of nature and arithmetic are united via a typical issue: all contain self-repeating shapes, or gnomons. nearly 2000 years in the past, Hero of Alexandria outlined the gnomon as that shape which, while extra to a couple shape, ends up in a brand new shape, just like the unique. In a spiral seashell, for instance, we see that every new element of progress (the gnomon) resembles its predecessor and keeps the shell's total form. encouraged by way of Hero, Midhat Gazale - a fellow local of Alexandria - explains the houses of gnomons, strains their lengthy and vibrant historical past in human suggestion, and explores the mathematical and geometrical marvels they make attainable. The textual content should still attract somebody attracted to the wonders of geometry and arithmetic, in addition to to fans of mathematical puzzles and recreations

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Additional info for A History of Numerical Analysis from the 16th through the 19th Century

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The causal explanation of me Industrial Revolution runs into similar quandaries. 31 It is not even certain that the question Why did the Industrial Revolution occur in Britain rather than in some otitaer country? is necessarily the best way to approach the material. For one thing, as we have already indicated, the Industrial Revolution was not so much a national as a regional affair. This has been stressed again in a collection devoted to this issue (Hudson, 1989). The regional argument was presented most cogently by Sidney Pollard (1981, 1985).

On the Continent, too, the evidence is mixed: Belgium, the first nation to adopt Britain's techniques, shared with her a wealth, of iron and coal; Switzerland, a close second, had neither. Buying coal and iron from other economies added to industrial costs, but such additions were, on the whole, sufficiently small to be dwarfed by other cost differences. In other words, it is possible to accept Wrigley's (1987) view that substituting coal for wood was an important part of the economic transformation of Britain, without attributing undue significance to the geographical accident of the presence of coal in Britain.

As soon as inventions became widespread rather than isolated they provided mutual support for each other... Technology had 'taken off*. " For that reason, we need to examine the details of Britain's economy and society to understand why she came to play the role she did. Geography Britain's geographical advantages over other economies have often seemed to be good explanations for its economic success after 1750. In one book, a social historian states it as self-evident that "England is built [sic] upon an underground mountain of coal.

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A History of Numerical Analysis from the 16th through the 19th Century by H. H. Goldstine

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