• A Slice of Pi History: How π Took Over The World

    Date:8 March 2019 Author: Brendon Petersen Tags:,

    Not every mathematical constant gets its own day. But not every constant is π.

    Pi Day got started in 1988 in San Francisco, when Larry Shaw, the legendary technical curator of the city’s Exploratorium, saw the connection between March 14 (3.14) and pi (3.14159…). Add in the fact that 3/14 is Albert Einstein’s birthday and you’ve got a ready-made celebration.

    Pi seems simple: It’s the ratio of a circle’s circumference to its diameter. Under the surface, though, it’s anything but. Mathematicians have spent centuries finding more and more digits of pi and discovering ways in which it intersects with the rest of mathematics.

    1.  It Wasn’t Always π

    Convergence Portrait Gallery Liu Hiu


    A mathematical constant like π can be seen as a part of nature, akin to a river or a grassy hill. It’s always existed, and mathematicians in a number of cultures discovered the number that becomes the area of a circle when multiplied by a radius squared.

    There are a number of claims on 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 Hiu, 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 3. Using a 96-sided polygon, Liu Hiu was able to determine that the ratio had to be greater than 3. In fact, he figured out the first five digits: 3.1416

    2. The Modern π

    William Jones


    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 endeavour. In 1706 he 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 began to advance in mathematical society, eventually befriending legendary names Isaac Newton and Edmund Halley. But the name didn’t stick.

    3. π Celebrities

    william shanks placeholder


    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 somebody 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 which 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.

    4. π and the Computer Era

    ibm 7090


    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 a half-million dollars 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 were able to use 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 8 hours and 43 minutes 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.

    5. A Supercomputer Slice of π

    Yasumasa Kanada


    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.

    And for the record, scientist Peter Trueb holds the current record: 22,459,157,718,361 digits, which he determined in 105 days. He used a homebuilt computer for the project.


    Originally published on Popular Mechanics

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