Since the beginning of mathematics mathematicians have been reevaluating ( to more and more decimal places. It has gone from a whole number to 134,217,700 digits after the decimal. ( is the ratio of circumference of a circle to its diameter. In the ancient orient ( was frequently taken as 3. Later the Egyptians gave ( a vale of (4/3)4=3. 1604. But the first scientific attempt to compute ( seemed to be that of Archimedes in 240BC.
He used polygons to set bounds for (, which he found o be between 223/71 and 22/7, or to two decimal places (=3. 14. His method was known as the classical method. In 150 AD the first notable value of (, after that of Archimedes, was given by Claudius Ptolemy of Alexandria in his famous Syntaxis mathematica he calculated ( to be 3. 1416. A Chinese mechanics worker in 480 gave the rational approximation 355/113 = 3. 1415929… , which was correct to six places. Al-Kashi in 1429 used the classical method to calculate ( to sixteen decimal places. was calculated o thirty-five decimal places by Ludolph van Ceulen of the Netherlands in 1610 using the classical method and polygons having 262 sides.
In 1621 Willebrord Snell, a Dutch physicist devised a trigonometric improvement of the classical method which allowed him to obtain considerably closer bounds. He calculated ( to thirty-five places like van Ceulen but with polygons with only 230 sides. Abraham Sharp in 1699 found seventy-one correct decimal places by using x=(1/3. In 1767 Johann Heinrich Lambert showed that ( was irrational.
William Rutherford calculated ( to 208 decimal places in 1841 but was later found that only 152 were correct. Zacharias Dase in 1844 found ( correct to 200 places. Dase was perhaps one of the most extraordinary mental calculators who ever lived. William Rutherford returned to the problem and found ( to 400 decimal places in 1853. ( was calculated to 707 places by William Shanks of England in 1873. this remained the most fabulous piece of calculation ever performed. D. F. Ferguson and J. W. Wrench jointly published a corrected value of ( to 808 laces in 1948.
In 1949 an army ballistic research laboratory computer in Aberdeen Maryland, known as ENIAC, calculated ( to 2037 decimal places. After 1949 computers were able to compute the value of ( to more and more places. In 1986 in a NASA research center in California a supercomputer calculated ( to 29,3600,000 decimal places. A little later Yasumasa Kanada of Tokyo used a NEC SX-2 supercomputer to compute ( to 134,217,700 digits passed the decimal. There are many reasons why mathematicians have been alculating ( to a great number of places.
Not only is it just a challenge but to see if digits in ( repeat, to find out if ( is simply normal or normal, and it is valuable in computer science to design better programs. I found this assignment not fun. Writing has been something I have always hated and math has not been one of my favorite subjects. So I disliked this assignment very much. As for the library’s math collection, I really can not comment on it because I simply chose the first math book I saw so I really don’t have any suggestions.
