MNEMONICS FOR THE NUMBER PI

There once was a fellow from Greece,
Who forgot pi's last decimal piece.
So he used electronics
To collect pi mnemonics ...
Now he's hooked, and there is no release.
Michael P. Masterson-Gibbons

School-children can always be found competing to see who knows the most digits of pi. My own interest and patience usually ran out at 3.14159. Pi is the ratio between a circle's circumference and its diameter. When expressed decimally it extends to infinity as a series of apparently random digits.

Pi = 3.1415926535897932384626433832795028841971...

Finding out pi's digits 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 (3 1/8) and Egyptian (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. The Indiana Pi Bill of 1897 would have legally established the value of pi. The wording is so murky that several conclusions are possible. Experts have argued for 3; 3.2; 4; and even a number greater than 9. The bill managed to get preliminary approval by the Indiana house, but was tabled by its senate after much public ridicule by local academics.

It is useful to scientists to know approximately the value of pi, perhaps to two or three decimal places. If it is required to a greater accuracy, then generally calculators and computers can be used.

You may question, then, the usefulness of mnemonics for memorising pi to many more digits. It can only be for the challenge itself. One gentleman, Hiroyuki Goto, recited no less than 42,000 digits of pi from memory in 1995. This record feat took him about nine hours to complete.

The most common type of mnemonic is the word-length mnemonic in which the number of letters in each word corresponds to a digit. This simple one gives pi to seven decimal places:

How I wish I could calculate pi.

This longer one, giving fifteen decimal places of pi, is popular with students:

How I like a drink, alcoholic of course,
after the heavy lectures involving quantum mechanics.

This little rhyme aids the memorisation of twenty-one digits of pi:

 Now, I wish I could recollect pi.
"Eureka," cried the great inventor.
Christmas Pudding; Christmas Pie
Is the problem's very center.

And if you feel the need for a device for remembering thirty-one decimal places of pi, try this rhyme:

Sir, I bear a rhyme excelling
In mystic force, and magic spelling
Celestial sprites elucidate
All my own striving can't relate
Or locate they who can cogitate
And so finally terminate.  Finis.

There is a problem with this type of mnemonic that does not affect the above examples. It is how to represent the digit zero. Fortunately a zero does not occur in pi until the thirty-second place. Several people have come up with ingenious methods of overcoming this, most commonly using a ten-letter word to represent zero. In other cases a certain piece of punctuation indicates a naught.

There are many stories and poems crafted in this way, and at least one encoding over 700 digits of pi.
 



Jill Britton Home Page
09-May-2005
Copyright Jill Britton