Lindemann concluded the problem of ‘squaring the circle’. Given a circle the
challenge was to construct a square of the same area using only a pair of
compasses and a straight edge. Lindemann proved conclusively that it cannot be
done. Nowadays the phrase squaring the circle is the equivalent of an
impossibility.
The actual calculation of π continued apace. In 1853, William Shanks claimed
a value correct to 607 places (actually correct up to only 527). In modern times
the quest for calculating π to more and more decimal places gained momentum
through the modern computer. In 1949, π was calculated to 2037 decimal
places, which took 70 hours to do on an ENIAC computer. By 2002, π had been
computed to a staggering 1,241,100,000,000 places, but it is an ever growing
tail. If we stood on the equator and started writing down the expansion of π,
Shanks’ calculation would take us a full 14 metres, but the length of the 2002
expansion would take us about 62 laps around the world!
Various questions about π have been asked and aswered. Are the digits of π
random? Is it possible to find a predetermined sequence in the expansion? For
instance, is it possible to find the sequence 0123456789 in the expansion? In the
1950s this seemed unknowable. No one had found such a sequence in the 2000
known digits of π. L.E.J. Brouwer, a leading Dutch mathematician, said the
question was devoid of meaning since he believed it could not be experienced. In
fact these digits were found in 1997 beginning at the position 17,387,594,880,
or, using the equator metaphor, about 3000 miles before one lap is completed.
You will find ten sixes in a row before you have completed 600 miles but will
have to wait until one lap has been completed and gone a further 3600 miles to
find ten sevens in a row.
π in poetry
If you really want to remember the first values in the expansion of π perhaps a little poetry will
help. Following the tradition of teaching mathematics in the ‘mnemonic way’ there is a brilliant
variation of Edgar Allen Poe’s poem ‘The Raven’ by Michael Keith.