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…
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Mathtuition88 