Thu 2024-Mar-14

Pi Day 2024

Tagged: Math / TheDivineMadness / ϜΤΦ

So… it’s Pi Day. Again. Didn’t we do this last year?

The Annual Tribal Observation

In honor of 3/14, as is the custom of our tribe:

\[\pi = 3 + \frac{1}{7 + \frac{1}{15 + \frac{1}{1 + \frac{1}{292 + \cdots}}}}\]

You can read off the continuands from the columns of this image, reading in binary from left to right [1] [2]: Continuands of pi simple continued fraction, in binary, columnwise

Dropping at the large continuand 292, we get the extremely good convergent $\pi = 355/113 = 3.14159292\cdots$, accurate to 7 significant figures (6 decimal places). The first known source for using this is the Chinese astronomer Tsu Ch’ung-Chih, in the 5th century CE. [3]

The Weekend Conclusion

But most importantly: Ceterum censeo, Trump incarcerandam esse.

Notes & References

1: EW Weisstein, “Pi Continued Fraction”, Wolfram MathWorld, retrieved 2024-Mar-14.

2: NJA Sloane, “OEIS 001203: Simple continued fraction expansion of Pi”, Online Encyclopedia of Integer Sequences, retrieved 2024-Mar-14.

3: M Gardner, New Mathematical Diversions from Scientific American, Chapter 8, “The Transcendental Number Pi”, pp 91-102, New York: Simon & Schuster, 1966.

Published Thu 2024-Mar-14

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