Pi: A Source Book - download pdf or read online

By Lennart Berggren

ISBN-10: 1441919155

ISBN-13: 9781441919151

ISBN-10: 1475742177

ISBN-13: 9781475742176

Pi is among the few techniques in arithmetic whose point out conjures up a reaction of popularity and curiosity in these now not involved professionally with the topic. but, regardless of this, no resource publication on Pi has ever been released. Mathematicians and historians of arithmetic will locate this publication critical. academics from the 7th grade onward will locate considerable assets for something from specified subject classes to person talks and exact pupil initiatives.

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Extra resources for Pi: A Source Book

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LbgJ. 1982. Jiu zhang suanshu zhengming wentide gai shu [cuJ [A summary of the various views on the Jiu zhang suanshuJ. , pp. 28-50. Beijing: Shifan daxue chubanshe. Mikami, Y. 1913. The development of mathematics in China and Japan. All page references are to the second edition, New York: Chelsea, 1974. Needham, J. 1959. Science and civilisation in China. Vol. 3. Cambridge: Cambridge Univ. Press. Neugebauer, O. 1952. The exact sciences in antiquity. : Brown Univ. Press, 1957. Qian Baocong [aIJ.

As an example, consider the sequence {an} defined by an - ~lf1ecoo'cosn(Jd(J. ) It is easily verified, on integrating (3) by parts, that this sequence satisfies the recurrence relation (4) an+l- an_I - 2oo n • In principle, given ao and a" we may then use (4) to compute the value of any all' In practice, the recurrence relation (4) does not provide a satisfactory method of computing this sequence, because it is numerically unstable. 1303, which are correct to 4 decimal places. 0057, as ... 0187.

Multiply this by the radius I chi and also by 24 to obtain 3139344000000 [square] hu. Divide by I()()()()()()()()()() to obtain 313~g!. Isquarel C"" which is the area of an inscribed polygon of 96 sides. Method of CUlling an inscribed polygoll of 48 sides illto olle of96 sides. Again, let the radius be the hypotenuse and half the side of the polygon of 48 sides be the gou. From this find the guo Put down the square of the hypotenuse of the preceding [triangle] and divide it by 4 to obtain 4277569703 [square] hu after the remaining terms are discarded, and this is the square of the gou.

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Pi: A Source Book by Lennart Berggren

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