Pi Number Approximation With Monte Carlo Method

Braincycle

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

Let us draw a circle with radius ‘r’

circles_dtheta

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

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

circle_square

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

https://mathtuition88.com/

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.