By Lennart Berggren
Pi is without doubt one of the few suggestions in arithmetic whose point out inspires a reaction of popularity and curiosity in these now not involved professionally with the topic. but, regardless of this, no resource ebook on Pi has ever been released. Mathematicians and historians of arithmetic will locate this booklet crucial. lecturers from the 7th grade onward will locate considerable assets for something from specified subject classes to person talks and unique scholar initiatives.
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Extra info for Pi: A Source Book
Sample text
AB : BF< 1009i : 66 ..................... (6). Therefore Fourthly, let the angle BAF be bisected by AG meeting the circle in G. Then AG: GB [=BA + AF: BF] < 2016! : 66, by (5) and (6). ] AB: BG < 20171: 66, Therefore BG : AB> 66 : 2017t ...................... (7). whence [Now the angle BAG which is the result of the fOUl·th bisection of the angle BAC, or of one-third of a right angle, is equal to one-fortyeighth of a right angle. ] Therefore BG is a side of a regular inscribed polygon of 9G sides.
The development o/mathematics in China and Japan . All page referenees are to the seeond edition, New York: Chelsea, 1974. Needham, J. 1959. Science and civilisation in China. Vol. 3. Cambridge: Cambridge Univ. Press. Neugebauer, O. 1952. l' in llntiqllity. : Brown Univ . Press, 1957. Qian Baoeong [al] . 1923. Zhongguo suan shu zhong zhi zhoulu yanjiu [ex] IA sludy of 7T in Chinese mathematical texts] . In Qian Baocong kexueshi IUllwen xuanji [ey) [Selected essays of Qian Baoeong on the history of Chinese seience], pp.
From this, find the gu. Put down the square of the smaller hypotenuse of the preceding [triangle) and divide it by 4 to obtain 17037087366 [square) /zu after the remaining terms are discarded, and this is the square of the KOU. Subtract this from the square of the hypotenuse and find the square root of the difference to obtain the gu, which is 9 cun 9 Jen lli 41wo 4 miao 4! hu. Subtract this from the radius to give a remainder of 8li 5 hao 5 miao 51 hu, which is called the smaller gou; half the side of the 24-sided polygon is called the smaller gu and from these, the smaller hypotenuse is derived.