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Thursday, March 12, 2015

Throwback Fact: Pi Day

This Saturday, March 14th, is known as the "Ultimate Pi Day" because the first 10 digits of pi (3.141592653) line up with an observable time: March 14th, 2015 at 9:26:53 AM or PM. 

But actually, all infinite digits are represented.

All of the digits after the first 10 are not quite observable. But about halfway between the 9:26:53 and 9:26:54, there will also be 58 centiseconds, 97 deciseconds, and so on until infinity.

This fact is exciting mathematicians into celebrating Pi Day even if they haven't bothered before. In fact, choosing March 14th to celebrate Pi annoyed a few mathematicians. Using 3.14 cuts Pi into a tiny approximation, and ignores everything that makes Pi incredible, like its transcendentalism.

Being transcendental marks Pi as similar to irrational numbers like the square root of two, but also more unique. The square root of two goes on and on forever- it is not capable of representation as the ratio of two integers. But the square root of two can be found as the result of algebraic operations. Pi, on the other hand, is impossible to be calculated this way. It cannot be found as the result of multiplication, division, exponentiation, addition, subtraction, or roots. Another transcendental number is e.

Have you ever considered how Pi is calculated? Pi is the ratio of a circle's circumference to its diameter. So are computers just hyper-accurately measuring circles?
The form of the Machin Formula
Well, no. This site [is ancient! But] gives a good explanation on the calculations: it's done most often by a converging series. Often, they follow patterns set by the Machin Formula of 1706, and the variations follow a basic form, as pictured above.

Our calculations of Pi have been getting more and more exact for thousands of years. The ancient Babylonians (here's the throwback section of this post!) had enough knowledge of Pi to approximate it to 25/8 = 3.125. The Egyptians, as discovered on the Rhind Papyrus, had knowledge of Pi and approximated the value as (16/9)^2 = 3.1605. Archimedes approximated Pi using geometry to a range between 3 + (10/71) and 3 + (1/7). The original Machin Formula got us to 100 digits of Pi, and as of December 2013, computers have calculated Pi to 12 trillion digits.

As cool as Pi actually is beyond 3.14, many people are content to simply acknowledge the day with a slice of pie. Which we totally plan to do.

Be on the lookout this Pi Day for the Center of Math's upcoming YouTube video- a Fun Fact compilation about Pi!

And don't forget to enter our Pi Day Giveaway, it ends tomorrow at 11 AM!

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