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As Simple as Pi
Most people's first slice of Pi is at school where it
is generally made palatable as either 3.14 or the fraction
3 1/7. The memory of this number may be fuzzy for those
propelled through their Maths GCSE by the power of Casio
(where Pi was reduced to a button on the bottom row
of the calculator), but the likelihood is they still
recall that romanticised notion of a number whose decimal
places randomly go on forever. At its simplest, Pi is
the ratio of the circumference of a circle to its diameter.
At its most complex, it is an irrational number that
cannot be expressed as the ratio of two whole numbers
and has an apparently random decimal string of infinite
length.
However, Pi's very "irrationality" makes it a prime
candidate for simplification, especially given its useful
nature. Wouldn't it be great if Pi was a simple short
decimal? No more need for that dodgy button on your
Casio. It was one such attempt at legalised reform that
amounted to a Pi in the face for the Indiana State Legislature.
In 1897 Edwin J. Goodwin, a sometime crank mathematician,
approached his State Representative with an interesting
proposition. Goodwin had drafted a self-styled "New
mathematical truth" which amongst other oddities claimed
that Pi was 3.2, which is not even accurate to one decimal
place. Moreover, Goodwin wanted to charge a royalty
to anyone who used his Pi, but if the State legally
recognised it, then he would exempt all Indiana textbooks
from paying the royalty.
He based much of his theory on that hoary chestnut of
squaring a circle (using a compass and ruler to find
a square with equal area to a given circle). Ironically,
it had only been 15 years since Ferdinand Lindemann
had proved that circles cannot be squared in such a
manner. Goodwin may have been ignorant of this glitch
in his theorising, but so were the Representatives of
the Lower House who passed the bill unanimously.
Fortunately C.A. Waldo, professor of mathematics at
Purdue University happened to be in the House on the
day of the bill's reading. When invited to meet Goodwin,
Waldo replied that he was already "acquainted with as
many crazy people as he cared to know." Waldo's timely
intervention spared the State Senate any further blushes
upon the bill's presentation to the Upper House. The
Senators, suitably primed by Waldo, peppered its reading
with derision and bad puns. After a half-hour of taxpayer
sanctioned frivolity it was decided to move for the
indefinite postponement of the bill.
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