Earl William Swokowski's Calculus with Analytic Geometry PDF

By Earl William Swokowski

ISBN-10: 0871503417

ISBN-13: 9780871503411

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Additional resources for Calculus with Analytic Geometry

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A variation of the same theme, less familiar to us in our usual thinking concerning “Pythagoras’ Theorem”, but even more in line with the way the Babylonians thought, is a proof derived from Fig. 7. Indeed, the Fig. a C b/2 D d 2 C 2ab; from which follows d 2 D a2 C b 2 : Fig. 7 The Putative Babylonian Proof of “Pythagoras’ Theorem” 20 2 The Great River Civilizations Such methods for dealing with sums of squares is well documented from Babylonian tablets. From [55, pp. 27–28], we reproduce the following example, to be found on a tablet in Strasbourg’s Biblioth`eque National et Universit`aire.

13 To find the area of a circle, the Egyptians squared the diameter and multiplied by 89 . What value for does this give? '/ for angles ' between 44ı 460 and 31ı 530 , or at least perhaps served a similar 1 purpose to such a table. '/ is very close to 60 from one line to the next. Assuming that Plimpton 322 were part of such a collection, try to compute the 15 numbers the preceding tablet would have contained. 1 Early Greek Geometry: Thales of Miletus The word geometry is derived from two Greek words, namely Á, g¯e, which means earth and " o , metron, which means measure.

Indeed, without secure knowledge on the changes of the seasons, it is not possible to sow the grain or other seeds at the right time. Sowing too early may destroy the crops by nightly frost early on, and sowing too late may not leave enough time for it to ripen. These needs were of the outmost importance, literally a question of life and death. And knowledge of a calendar is not possible without insights in astronomy, which again requires knowledge of geometry. Geometry and mathematics did also play an important role in measuring land, constructing irrigation channels or dykes along major rivers and in other engineering tasks.

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Calculus with Analytic Geometry by Earl William Swokowski

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