16-05-2014, 12:50 PM
π and How to Calculate its Values
What is π?
Pi or π is the Ancient Greek word/symbol used for the ratio between the diameter f a circle. In educational circles its value is used as a fraction (22/7) or as a decimal calculated up to 2 decimal places(3.14). The earliest calculator of the value of π was Pythagoras who calculated it up to 5 decimal places. It is an invaluable value in the method to calculate the circumference and area of circles, cones, cylinders, spheres and many other shapes. By using the equations created by the great Indian mathematician Ramanujan and modern super computers it has been possible to calculate the value of π into trillions of places the record being calculated the Johnson-Cray supercomputer of NASA calculating its value into11x1013 decimal places.
Circle Method
This is one of the oldest and the most conventional method to calculate the value of π . A circle with a pre known diameter is drawn and a point A is taken on the perimeter or circumference of the circle. Then the circle is rotated and the point A is rotated along with it. Thus the distance covered by the point = the circumference of the circle. We can do this with a string too. Now we use the formula
Circumference©=2π x radius® or Diameter(d) x π
The value of Diameter(D) and Circumference© is already known and from this we can calculate the value of π.
Polygon Approximation
This is the oldest method to calculate the value of π, and also one of the simplest as it only requires a base knowledge of mensuration, division and decimals. This method was devised by the Greek mathematical genius Archimedes. and was in use for 1000 yrs. For this reason π is still sometimes known as the “Archimedes’ Constant”.
In this method we draw any polygon with a circle inside it and another polygon of the same type as other within the circle .
Then we will get the perimeter(p) of both the polygons of both the polygons and by dividing p of the bigger
polygon with p of the smaller polygon we get the value
of π
* The more the sides of the polygon the closer we will get to the value of π
Piphiliology
A new branch of mnemonic study opened up by the existence of pi is piphiliogy that is the ability to memorize maximum no. of digits of pi
. Though the practical need for the digits of pi only extend to the first five digits of pi (3.14159) people have memorized its value up to a thousand digits and more due to the ingrained psychology of humans to break records.
The current piphiliological record belongs to Chinese wunderkind Lu Chao who recited 67,890 digits of pi in 24 hours and 4 minutes on 20 November 2005.
Also the record for the calculation of pi up to most number of decimal places by any means goes to the Japanese supercomputer T2K Open Supercomputer, located at theUniversity of Tsukuba’s Center for Computational Sciences which has calculated its value up to its 2.8 trillionth decimal place.