## Shotgun PiMay 5, 2014 I've had an interest in the mathematical constant, pi, since I first learned of it in elementary school. Since I've published a book about pi this year, it's apparent that this interest still holds. Although just a few digits of pi are required in any scientific or practical calculation, pi has been calculated to ten trillion (10^{13}) digits. I reviewed some simple analytical and physical methods of estimating the value of pi in a previous article (Another Piece of Pi, July 28, 2010).
The observable universe is a sphere with a diameter of about 9 x 10^{26} meters. This means that only 27 digits of pi are needed to calculate its circumference to better than a meter. Since the size of a hydrogen atom is about 100 picometer (10^{-10} meter), only 37 digits of pi are needed to calculate the circumference of the universe to the size of an atom.
The fraction, 22/7, is a close approximation to the value of pi, as Archimedes discovered by circumscribing polygons around a circle, noting their perimeter P, and taking a ratio to the diameter D of the circle to get π ≈ P/D. Archimedes obtained his estimate of 22/7 (3.142857...) for pi using a circumscribed 96-sided polygon. Ptolemy improved Archimedes' estimate with a 360-sided polygon, obtaining 3,141666..., a value that's correct to three decimal places.
## References:- Vincent Dumoulin and Félix Thouin, "A Ballistic Monte Carlo Approximation of π," arXiv Preprint Server, April 8, 2014.
- How Mathematicians Used A Pump-Action Shotgun to Estimate Pi, The Physics arXiv Blog.
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