When Shanks published a small book on pi in 1853, he dedicated it to Rutherford, “from whom I received my earliest lessons in numbers.” It turns out that Rutherford taught at a school not far from Corsenside in the 1820s. It’s true that Shanks studied with Rutherford, but this was not the relationship of a graduate student with a thesis advisor. Some sources identify Shanks as a student of William Rutherford, a mathematician who taught at the Royal Military Academy and also dabbled in pi calculations. After his marriage he lived in Houghton-le-Spring, another small northeastern town, where he ran a boarding school. He came from Corsenside, a village in the northeast of England, near the Scottish border. It’s known that he was born in 1812, married in 1846, and died in 1882. I think I also know where a couple of his errors crept in, but there are more that remain unexplained.īiographical details about William Shanks are hard to come by. But by adapting some pencil-driven algorithms to run on silicon computers, I have gotten a glimpse of what the process might have been like for Shanks. I haven’t the stamina for that-or even the life expectancy. One way to answer these questions would be to buy several reams of paper, sharpen a dozen pencils, and try to retrace Shanks’s steps. Who was this prodigious human computer? What led him to undertake his quixotic adventures in arithmetic? How did he deal with the logistical challenges of the pi computation: the teetering columns of figures, the grueling bouts of multiplication and division? And what went wrong in the late stages of the work? I have long been curious about Shanks and his 707 digits.
Scientists calculate pi digits series#
Shanks made a series of mistakes beginning around decimal place 530 that spoiled the rest of his work. Moreover, the laptop will give theĭigits. Anyone with a laptop can compute hundreds of digits of pi in microseconds. All his patient toil has been reduced to triviality. When was humanity’s calculation of pi accurate enough for NASA? In 1424, Persian astronomer and mathematician Jamshid al-Kashi calculated pi to 17 digits.Seen from a 21st-century perspective, Shanks is a poignant figure. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.
It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. We don’t need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. Let’s say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. The most distant spacecraft from Earth is Voyager 1. How precise are calculations with that number? This precise: NASA’s Marc Rayman explains that in order to send out probes and slingshot them accurately throughout the solar system, NASA needs to use only 15 decimal places, or 3.141592653589793. Mathematicians have calculated pi out to more than 13 trillion decimal places, a calculation that took 208 days.
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