Pi Number
A little known verse in the bible reads "And he made a molten sea, ten cubits
from the one brim to the other; it was round all about, and his height was five
cubits; and a line of thirty cubits did compass it about (I Kings 7, 23)."
This passage from the bible demonstrates the ancient nature of the irrational
number pi. Pi in fact is mentioned in a number of verses throughout the bible.
In II Chronicles 4,2, in the passage describing the building of the great temple
of Solomon which was built around 950BC, pi is given as equal to three. This
value is not very accurate at all and should not even be considered accurate for
it’s time, however it should be noted that precision was not needed for the
task that was being performed and we should let the general concept of pi that
the biblical characters posses impress us. Present knowledge suggests that the
concept of pi first developed in 2000 BC in two separate cultures. The
Babylonians used pi at a value of 25/8 while an entirely different culture, the
ancient Egyptians used pi at a value of 256/81. While the biblical calculation
of pi=3 most likely came from crude measurement, there is strong reason to
believe, because of the relative accuracy of the values, that the Babylonians
and Egyptians found pi by means of mathematical equations. In the Egyptian Rhind
Papyrus, which is dated around 1650 BC, there is strong evidence supporting that
the Egyptians used 4(8/9)2 =3.16 for their value of pi. At that point in
history, and for the majority of modern history, pi was not seen as an
irrational number as it is today. The next culture that investigated pi was the
ancient Greeks. Starting in 434 BC Greeks were unraveling the mysteries of pi.
The mathematician Anaxagoras made an unsuccessful attempt at finding pi, which
he called squaring 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
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