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

venn pi

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’.

f8565d2a-dacf-4c07-b543-42bd8c966adc-1024x768

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

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4 comments

  1. 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 🙂

    Liked by 1 person

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