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Thursday, May 21, 2015

Throwback Fact: The Origins of Pi

We've mentioned pi quite a few times on the blog (our pi day post in particular). However, we've never discussed the reasoning behind the symbol.

Pi, of course, has existed in approximations since the time of the Babylonians (who got to 28/8 = 3.125) and the Ancient Egyptians (who found (16/9)^2 = 3.1605 on the Rhind Papyrus). Approximations have become better and better over time, but it will never end. Pi is transcendental- it is irrational, and cannot be found as the result of an algebraic function. We can continue to calculate more and more digits, but the number of trailing digits is an uncountable infinity, and therefore we will never know exactly what pi is.

A number such as this seems like it shouldn't be useful. We don't have a true value for pi, and it seems too cumbersome to use in everyday math. Yet, pi is used every single day, for children in middle school and beyond. [Sidenote: Does anyone remember when they learned about pi? I don't have a specific memory of learning it- it's just there. Please share your thoughts in the comments!]

William Jones
The incredibly common usage of pi brings forth an even more strange fact about the number: until 1706, there was no uniform symbol in use for pi, and it didn't have a name. That year, a math teacher by the unassuming name of William Jones realized that he believed that pi was irrational.  The proof didn't come until 1761 by mathematician Johann Lambert, but Jones realized that pi was being misrepresented in the texts of the time. It was common for pi to simply be written as (22/7) or (355/113), which may lead to the belief that it is a rational number. Because pi could not be represented as a ratio of two integers, it needed a symbol to represent an unreachable ideal.

Jones chose the greek letter Pi to represent the quantity which, when the diameter is multiplied by it, yields the circumference of a circle. We only wish he had made this decision on March 14th- it would have made a great Pi Day fact even better.

If you like learning about pi as much as we do, check out our humorous Pi Day video from this past March! We hope it'll make you laugh. Let us know about your experience with pi in the comments.

1 comment:

  1. When I participated in a conference on ancient and modern approaches to music in New Delhi in 1970, the pundits argued over the number of small intervals there were in an octave—they all agreed on seven primary intervals.
    One of them proposed that the correct number is twenty-two, because "22/7 is π".