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*A Quickie on Pi*

*A Quickie on Pi*

March 14, 2017

The famous symbol: π is used extensively in geometry. It was introduced by British mathematician William Jones in 1706 who wrote that π = 3.14159. But the ratio of the circumference of a circle to the diameter of that circle has been known for thousands of years. The ancient Babylonians usually estimated the area of a circle equating π with 3, but one tablet from dating between 1900 and 1680 BCE uses the value of 3.125 for pi. In ancient Egypt, the formula [(8d)/9]2 was used to calculate the area of a circle, and approximates π to 3.1605. Archimedes, who lived from 287 to 212 BCE, performed the first theoretical calculation of π and found the following: 223/71 < π < 22/7. He did so by finding the area of a regular polygon inscribed within a circle and the area of a regular polygon within which the circle was inscribed.

Since Archimedes, there have been several attempts to estimate pi. James Gregory came up with a way to represent π/4 as a series, but it is not usable since even the sum of the first 5 million terms only return an estimate of six decimal places. The version of pi which is used in modern calculators is: π/4 = 4arctan(1/5) - arctan(1/239) and was discovered by John Machin. Mathematicians have even developed wacky techniques such as one called Buffon’s Needle that involves dropping needles and probability to calculate Pi.

I encourage you to learn more about a this mathematical icon (and homophone for a delicious dessert).

From the Quanta Staff and me, happy Pi Day!

Image Sources: Nicole Kim, http://delphiforfun.org/programs/images/Archimedes1B.png

About the Author: Jeremy Gleeson

Jeremy is a member of the Class of 2018 from California, USA.