Today, let's talk about 
-- and not the kind you eat. The University of
Houston's College of Engineering presents this
series about the machines that make our
civilization run, and the people whose ingenuity
created them.
School-children can always
be found competing to see who knows the most digits
of pi -- the ratio of the circumference of a
circle to its diameter. My interest and patience
usually ran out at 3.14159256. But finding out what
those digits were has been a major mathematical
challenge ever since the invention of the wheel
first stirred a real interest in circles. The
earliest recorded values of pi were Phoenician and
Egyptian. They were 3 1/8 and 3 13/81. Both values
are accurate within a half a percent.
Where did these values came from? From
measurements? Well, try measuring pi with a piece
of string. You won't come this close. The Hebrew
peoples used a rough empirical value of pi in the
Bible. It was three, and it's found in a text that
shows up in both the 1st Book of Kings and the 2nd
Book of Chronicles:
And he made a molten sea, ten cubits from the
one brim to
the other: It was round ... and a line of thirty
cubits
did compass it ... about.
From time to time you hear stories about
legislative bodies that've tried to make pi = 3 into
law on the basis of this text. Science writer Petr
Beckmann was unable to verify any of these stories,
but he does report a remarkable event in the 1897
Indiana State Legislature. An Indiana doctor thought
he'd solved the classical problem of squaring the
circle. That means specifying the size of a square
with the same area as a circle. If you could do that,
you'd also be able to get an exact value of pi. This
fellow tried to get his proof enacted as law. But the
text of his bill was muddled. It would've made pi
greater than nine.
The House had trouble finding anyone to review the
bill. They finally gave it to the Committee on
Swamp Lands, who said it looked okay to them. When
it cleared the House, the Senate gave it to their
Committee on Temperance. Temperance could no more
figure it out than Swamps could, so it got
preliminary approval. After that, local academics
heard of what Congress was up to and started
questioning legislators. The Bill mysteriously
disappeared from sight and was never heard from
again.
All this happened 15 years after mathematicians had
shown it was impossible either to square the circle
or to evaluate pi exactly. That's bizzare enough,
even if fundamentalists didn't really try to make
pi = 3 into law. But historians have also found out
that the accurate Phoenician and Egyptian values of
pi didn't come from measurements after all. These
ancient engineers actually deduced them, and they
used elegant geometry and logic to do it. It's a
sobering fact that they had clear-headed answers to
questions that still troubled a lot of people 4000
years later.
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.
(Theme music)
