Pi
The History of Pi 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.
