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.
Once upon a time, it was a common
sport for school children to compete over who knew the
most digits of the mathematical constant, Pi (or
). (That's
the ratio of the circumference of a circle to its
diameter.) My interest and patience usually ran out at
3.14159265.
But finding out what those digits were has been a major
mathematical challenge, ever since the invention of the
wheel began stirring a real interest in circles. The
earliest recorded values of were Phoenician and Egyptian.
They were 3 1/8 and 3 13/81. Both values are accurate
within half a percent.
Where did those numbers come from -- from measurements?
Well, you just try measuring with a piece of string. You won't
come that close. The Hebrew peoples suggested a rough
empirical value of in the Bible. It was three, and you'll find
it 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 enact laws, based on this text,
making
exactly equal to three. Science writer Petr Beckmann was
unable to verify any of these stories, but he does report
a remarkable event that took place 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 and a circle that both have the same
area. If you could do that, you'd also be able to get an
exact value of . This fellow tried to get his proof enacted as law,
but the text of his bill was muddled. It turns out that
it would have made 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 what Congress was up to
and started questioning legislators. The Bill
mysteriously disappeared, and it was not heard from
again.
All this happened fifteen years after mathematicians had
shown that it was impossible either to square the circle
or to evaluate exactly. That's bizarre enough, even if extremists
hadn't really tried to make it a law that was equal to
three. But historians have also found out that the
accurate Phoenician and Egyptian values of hadn't come from
measurements after all.
These ancient engineers actually deduced their values,
and they used elegant geometrical logic to do it. It is a
sobering fact that they had clear-headed answers to
questions that still troubled a lot of people four
thousand years later.
I'm John Lienhard, at the University of Houston, where
we're interested in the way inventive minds work.
(Theme music)
