Download Pi: A Source Book by Lennart Berggren PDF
By Lennart Berggren
Pi is without doubt one of the few suggestions 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 e-book on Pi has ever been released. Mathematicians and historians of arithmetic will locate this booklet critical. academics from the 7th grade onward will locate plentiful assets for whatever from unique subject classes to person talks and exact pupil tasks.
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Some ancient values of pi and their use in India. Mathematics Education 9, 1-5. He Shaogeng [bbl. 1983. Method for determining segment areas and evaluation of 1T. In Ancient China's technology and science. Compiled by the Institute of the History of Natural Sciences, Chinese Academy of Sciences. Beijing: Foreign Language Press. Heath, T. L. ). 1897. The works of Archimedes. All page references are to the reissued edition, New York: Dover, 1953. - - 1921. A history of Greek mathematics. 2 vols. London/New York: Oxford Univ.
3. The genius of Archimedes is displayed in his method. Without knowledge of subjects such as decimal notation and trigonometry, he was able to devise a method with inscribed and circumscribed polygons of 96 sides which gave the 22 328 LAM LAY-YONG AND ANG TIAN-SE HM 13 values of 11' as greater than 3 tV- but less than 3 ~. His method of calculating the approximate values of irrational square roots is still in the realm of speculation. Compared with Archimedes' method, then, Liu's method is simple and elegant.
The area of the inner square is half the area of the outer squarc. If the area of the circle is 157 [square units) then the area of the inscribed square is 100 [square unitsj. Next, if the diameter, 2 chi, is compared with the circumference, 6 chi 2 cun 8 fen, the ratio of the circumference to the diameter is obtained as 157 to 50. Actually, the circumference still has other smaller units. [Section 3] There was in the armory of the Jin dynasty a copper hu [cm] measure constructed by Wang Mang [ai) during the Han dynasty.