The History of Pi: How The Number Took Over The World

There are several claims to the very first discovery of Pi. Historians point to Babylonian and Egyptian cultures as likely discovering the concept around the year 2,000 B.C. Archimedes further specified it around 250 B.C., in his treatise Measurement of a Circle.

In 250 A.D., Chinese mathematician Liu Hui, in a work known as The Nine Chapters on the Mathematical Art, determined that the ratio of the circumference of a circle to its diameter had to be greater than three. Using a 96-sided polygon, Liu Hui determined that the ratio had to be greater than three. In fact, he figured out the first five digits: 3.1416.

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In the West, Archimedes became known as the constant’s discoverer. For centuries, 22/7 (a fractional approximation of pi) was primarily known by a full Greek name, περιφέρεια. That translates to “periphery,” which makes sense given how the constant relates to a circle.

But in the early 1700s, Welsh mathematician William Jones decided to simplify the entire endeavor. In 1706, Jones published Synopsis Palmariorum Matheseos, a beginner’s text on calculus and infinite series. Since the constant is infinite, Jones began shortening it to just π. Jones eventually advanced in mathematical society, befriending legendary names Isaac Newton and Edmund Halley. But the name didn’t stick.

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Soon, π started down its road of mathematical stardom. The idea of an endless number was appealing to many, especially amidst the bloom of scientific and technological discoveries made during the Industrial Revolution. For some, like William Shanks, π became an obsession. Shanks was born in 1815 in rural England. Not much is known about his life, but he became the master of a private boarding school in a small village called Houghton, mainly known at the time for coal mining. That didn’t interest Shanks much, though. Instead, during his free time, he devoted himself to calculating and determining more and more digits of π. He wasn’t a mathematician, but that didn’t stop him from spending his mornings building out calculations and his afternoons checking them.

Over time, he made impressive progress. In 1853 he published a book titled Contributions to Mathematics, Comprising Chiefly the Rectification of the Circle that gave 607 decimal places for π, the first 500 of which had been independently verified.

In 1873, Shanks reached the height of his π powers. He calculated 707 decimal places, a record that stood until the advent of the electronic computer. But there was a further indignity—in 1944, a mathematician named D.F. Ferguson independently went through Shanks’ work. There was a mistake. Ferguson discovered that Shanks had misplaced two terms, which threw off his 528th number.

The raw processing power of computers would forever change mathematics. Two mathematicians offered an early showcase of that power in 1962, with help from an early computer, the IBM 7090. First released in 1959, the 7090 was a fully transistorized system. That was a brand new concept in 1959 when most computers still used vacuum tubes, and the 7090 could make calculations six times faster than those vacuum tubes. It could be rented for a mere $63,500 per month (around $700,000 in today’s money).

Clients for the 7090 were mainly institutional, like the Department of Defense and NASA. In 1961, mathematicians Daniel Shanks and John Wrench used one to reach digits of π that William Shanks could not imagine: 100,000. According to the academic paper showing their work, it took the 7090 computer eight hours and 43 minutes to make the calculations. That may seem like a long time, but when compared to Shanks’ lifetime of work on the subject, it’s easy to see how the computer would revolutionize math. π marked an early success for the 7090, but not the last. Versions of the 7090 would later power the Gemini and Mercury space missions.

The obsession with π has continued into the modern era. Because it is an irrational number, this is no end to π, and the chase can continue indefinitely. Across the globe and centuries apart, Shanks found a common soul in Yasumasa Kanada, a professor in the Department of Information Science at the University of Tokyo. In 2002, Kanada set a new record: π to 24 trillion decimal places.

It took five years for Kanada’s team to develop the program used to get their result. And while their record has been broken in the years since, Kanada’s effort shows why the π fascination persists. At a certain point, the number lacks any practical or even academic use. But the challenge of reaching higher with it shows a human determination that has spanned the centuries. Today, the record stands at a whopping 62.8 trillion decimals.

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