# Pi Day 2016!

π is the constant ratio of the circumference to the diameter of any circle. The first 6 digits of π are 3.14159, which rounds up to 3.1416, corresponding to 03/14/16 or the 14th March, which is today! To celebrate I thought I’d write a post on this wonderfully useful, irrational number.

### ORIGIN

The number represented by π appears in our earliest historical records of mathematics. For example, Babylonian clay tablets (1800 – 1650 BCE) discuss how a circle’s area could be determined from its circumference by using a constant, which is equivalent to 3.125. Additionally, the Rhind papyrus (around 1650 BCE) mentions a π-like constant with the value of about 3.16 in the context of geometrical problems involving finding a square equal in area to a given circle.

However, perhaps the first to provide a theoretical calculation of π was Archimedes of Syracuse (287 – 212 BCE) who discussed the ratio of a circle’s circumference and diameter. Then, by using a series of polygons inscribed in a circle and another circumscribing it, he was able to determine that π was about 3.1418.

Since then, mathematicians have made the conclusion that pi does not have an exact value – its decimal value extends on infinitely without a repeating pattern, meaning that it is an irrational number.

### FACTS

1. If you were to print 1 billion decimal values of π in ordinary font it would stretch from New York City to Kansas.
2. At position 763 there are six nines in a row, which is known as the Feynman Point.
3. The fraction 22/7 is a well-used number for π, and is accurate to 0.04025%. However, the most accurate fraction of π is 104348/33215, which is accurate to 0.00000001056%!
4. William Jones (1675-1749) introduced the symbol “π” in the 1706, and it was later popularised by Leonhard Euler (1707-1783) in 1737. For more on this I recommend this article!
5. This number’s uses stretches beyond just mathematics; Pi appears in the physics that describes waves, such as ripples of light and sound, and enters into Heisenberg’s uncertainty principle. Additionally, even the average meandering ratio of rivers approaches π!

### PHOTOS

Source: The Guardian

In The Logic of Chance (1888), Victorian mathematician John Venn suggested that the digits 0 to 7 represent eight compass directions, and by following the path tracked by these digits in pi, missing out the first 3, this image was created. This type of image is called a ‘random walk’.

Source: The Guardian

Francisco Aragón and his colleagues converted pi into base 4 and tracked a random walk of pi for 100 billion digits.

Source: mkweb.bcgsc.ca

Distribution of the first 13,689 digits of π by Martin Krzywinski.

Hope you enjoy the rest of the day! M x

1. Sorry, I think I phrased that incorrectly! It should be ‘a more accurate fraction’. The accuracy was measured by comparing it with a long chain of the decimal places pi 🙂

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2. I think the statement “The fraction 22/7 …. is accurate to 0.04025%. However, the most accurate fraction of π is104348/33215, which is accurate to 0.00000001056%!” is wrong.

Since, you can’t define “most” accurate value of an irrational number and how did you calculate accuracy? Please give references.

Happy Pi Day 🙂

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1. If you compare it with another million digits it is accurate enough though this is certainly a good point!

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