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 pi was incorrect. Soon after in
1948, Ferguson and Wrench published the correct value of pi to 808 decimal
places. However in 1949, with their computer up and running, Ferguson and Wrech
were able to find pi to it’s most exact value ever.
