Pi Number Approximation With Monte Carlo Method


Pi(Π) number is irrational and equal to 3.14159265… .                                    

Let us draw a circle with radius ‘r’


$latex \int_0^{2\pi} r \mathrm{d}\theta = {2\pi} r &s=2$

So, circumference of the circle is equal to $latex {2\pi} r $

If the value of circumference is divided by value of diameter, the result is $latex \pi $

Area of quarter circle = $latex \frac{\pi r^2}{4}&s=2$


Area of the square = $latex {r^2}&s=2$

Probability of putting a dot on quarter circle is shown below.

$latex \frac{\frac{\pi r^2}{4}}{r^2} = \frac{\pi}{4}&s=3$

The area of circle is divided by total area.

In order to achieve $latex \pi $ value the result is multiplied by 4.

We can use Monte Carlo method for approximation $latex \pi $ value. For example, 10000 dots will be put on picture above. Each dot…

View original post 47 more words

Author: mathtuition88


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