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#
estimate pi using random numbers

pi is an **irrational number** and it has infinite decimal places

we will use the concept of probability and definition of pi to calculate the value of pi

## steps to do so

### make a unit circle enclosed within square touching its boundaries

### randomly plot points inside the square

### count the number of points that lie inside the circle and total number of points

## calculation of Pi

### how probability works

since we are randomly plotting points inside the square, the probability of it lying inside the circle is

** area of circle / area of square **

## how does counting help

since we are plotting many points, empirical probability says that

** P = number of points inside circle / Total number of points **

## using this to find Pi

since we know the empirical probability we will use it to find value of pi

ie. n/N = Pi/4

**Pi = 4(number of points inside circle / Total number of points)**

## conclusion

this is also know as Monte Carlo method, this works perfectly when number of pounts is fairly high

## sources

### SDE skills

### Stealthcopter

stealthcopter

### stackoverflow

stackoverflow

### geeks for geeks

geeks for geeks