pi
...quaring the circle and in 414 BC, 20 years after Anaxagoras failed in his attempt to square the circle, Aristophanes refers to the work of Anaxagoras in his comedy “The Birds”. It took over 100 years for the Greeks to finally find a value for pi. In 240 BC Archimedes of Syracuse showed that 223/71*pi*22/7. Archimedes knew, what so many people today do not, that pi does not equal 22/7 and he made no claim to have discovered the exact value of pi. However if we take the average of his two bounds we obtain pi=3.1418, which was an error of about 0.0002. Archimedes found the most accurate value of pi up to that time and his value would be used exclusively until the next discovery in the world of pi. The next major finding concerning pi did not occur in the western world, but in China by Tsu Chung-chi’h who approximated pi at 355/113 in 480 AD. Next to nothing except for this work is known about Tsu Chung-chi’h’s life but it is very unlikely that he had any awareness of Archimedes work. We shall now notice how during the dark ages of Europe, the lead in the research of pi is passed to the East. Aryabhata, working on his own in Persia without any outside information in 515 AD was able to approximate pi to 3 decimal places. A mathematician from Baghdad named Al’Khwarizimi worked with pi however the most accurate finding of pi to date was found even more east in Samarkand by Al-Khashi. In 1430 AD he approximated pi to 16 decimal places, the most to date. His work however, would be the last of note from the east as the European Renaissance brought about a whole new mathematical world. The first notable discovery in the approximation of pi from the European Renaissance was by Viete in 1593 AD. He expressed pi as an infinite product by using only 2’s and square roots. In 1610 Ludolph van Ceulen demonstrated the new thought coming out of the Renaissance by calculating pi to 35 decimal places. Around the same time, Snell refined Archimedes’s method of calculating pi, and Snell’s work was used by Grienberger to calculate pi to 39 decimal places in 1630. In 1655 Wallis showed that pi/2=2/1*2/3*4/3*4/5*6/5*6/7*8/7*8/9..... The 18th centuary brought about great achievements in the calculating of pi. In 1706, Machin found pi to 100 decimal places, the first time that feat was ever achieved and in the same year, a British mathematician, William Jones first used pi for the circle ratio. In 1737, Euler first used the Greek letter pi to represent the mysterious number therefore giving it it’s present day name. Up until the 18th centuary, pi was seen as a rational number, however in 1761, Lambert showed that pi was irrational, therefore opening up a whole new world for the research of pi. Pi became seen as a boundless number, open for limitless exploration. Soon after Lambert’s discovery, Legendre showed that pi2 is irrational. The 19th centuary presented two mathematicians, who, without computers were able to find pi to huge amounts of decimal places. In 1844, Johann Dase, who was described by his contemporaries as “the lightning calculator” found pi to 200 decimal places. Shanks soon overshadowed Dase’s findings however by finding by to an astounding 707 decimal places in 1873. While the 19th centuary showed great strides in the calculation of pi, the 20th centuary, with the advent of computers, broke great barriers in finding the most exact value of pi. In 1945, two scientists, Ferguson and Wrench worked on a computer system for calculating pi, however before this system was perfected, they did some manual calculations. In 1945 Ferguson found that the number occupying the 528th place for Shank’s value of...