Engines of Our Ingenuity

No. 180:   PI

by John H. H. Lienhard

Click here for audio of Episode 180.

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)


Beckmann, P. A History of Pi. St. Martin's Press, New York, 1971.

      pi = 3.14159 26535 89793 23846 26433 83279 

             50288 41971 69399 37510 58209 74944 

             59230 78164 06286 20899 86280 34824 ...



      pi is very nearly = 355/113 = 3.14159292...  

This episode has been rewritten as Episode 1645.


The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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