## Michael Keith

### Circle Digits - A Self-Referential Story

from The Math. Intell. 8 (3), 56

The previous self-referential story is a mnemonic for the first 402 decimals of the number pi. As it indicates, merely count the number of letters in each word of the story (beginning with the first word, "For", up to and including the final words, "The End") to obtain the successive decimals to pi. Any punctuation mark other than a period represents a zero digit (a period stands fno digit). Words of longer than 9 letters represent two adjacent digits (for example, a twelve-letter word represents the two digits 1- 2). A digit written literally stands for the same digit in the expansion. This feature is only used once in the story (the first sentence of the seventh paragraph); overuse of this feature would be considered "cheating".

As far as I can determine, this story establishes a new record length for a literary pi mnemonic, although clearly the length of such a mnemonic is limited only by the patience of the constructor. This story has the added twist of self-reference, as it describes within itself its title, its method of construction, its length, and its subject. Incidentally, it has been checked by a computer program for correctness to the decimals of pi.

For those who want to compose even longer mnemonics using the same or similar rules, the following points may be of interest:

1. At decimal 601, the first triple-zero occurs. Clearly we can handle this with the present scheme, but a little ingenuity is required. No quadruple-zeros occur within at least the first 10,000 decimals, so we don't have to concern ourselves with that possibility.

2. At decimal 772 we encounter the amazing sequence 9999998. This seven-digit group has the largest digit sum of any seven-digit group in the first million decimals! Because of the resulting requirement for seven adjacent long words, it also poses quite a challenge in encoding.
We have seen pi-mnemonic sentences, poems, and now, a short story. Perhaps some day a complete novel?

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