Calculating Pi (π)

Using the Monte Carlo Method.

How it Works:

The Monte Carlo method is a method of computing Pi(π). The way it works is by creating a small arc inside a square. The square should have a circle in it that covers it from top to bottom. A small arc will be placed in a random location of this square. If the arc lands inside of the circle, the amount of circles inside increments by one. To calculate π you must do the following formula:

π = 4 × (Points Inside Circle ÷ Total Points)

The higher the values the closer it is to π. Press the start button to start the animation.

Canvas is not supported.
Points Inside: Points Outside: Total Points:
0 0 0
Value of Pi(π)
0

What is Pi?


Pi is a mathematical constant, the ratio of the circumference of a circle to its diameter.


In the 5th century BC, the Greek mathematician Archimedes was trying to find an accurate way to measure the size of a circle and eventually stumbled upon this ratio. He used that knowledge to calculate an approximation for Pi that was correct to two decimal places.


What we know as Pi was not given this name until 1706 when Swiss mathematician Leonhard Euler came up with it while working on some problems in geometry.


The symbol π has been in use since 1737 when another Swiss mathematician Johann Heinrich Lambert used it in his book "Lectiones Geometricae".




Ancient Greece and the Origins of Pi


The story of pi starts with the Ancient Greeks. They were the first group to truly explore and discuss the concept and properties of π. Scholars estimate that π was calculated to 14 decimal places by Archimedes in 225 BCE. The story continues with other mathematicians such as Tsu Ch'ung-chih found a way to calculate pi using what we now know as the "method of exhaustion".


Pi is an irrational number that can never be expressed exactly as a ratio between two integers (e.g. 3:2).




Calculating Pi Using Monte Carlo Method


The Monte Carlo method is a solution to calculating pi (π), it is often used in computational sciences. The method begins with the selection of random points within the unit square, then the average of these points are calculated. This process is repeated many times, each time drawing new points. Once enough calculations have been completed, the actual value for π can be approximated.




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