Calculating Pi using the Monte Carlo method

P_o = πr²

P_□ = a² = (2r)² = 4r²

 P_o      πr²
—— = ——
 P_□      4r²

 P_o      π
—— = —
 P_□      4

 P_o      k
—— ≈ —
 P_□      n

 π     k
— ≈ —
 4     n

         4k
π ≈ ——
        n

Implementation of the algorithm in language: Pascal, C++, Java, Python, JavaScript

1. START - The beginning of the algorithm.
2. We read the number of points to be generated (sampled).
3. We reset k - the counter for points contained within the circle of radius 1 (set k=0). We assign the initial value of 1 to the variable i, which counts the number of points sampled (set i=1).
4. We generate two random numbers in the range from 0 to 1 - the x and y coordinates of the point.
5. We check if the sampled point with coordinates x,y lies within the circle of radius 1. (Is x2+y2≤1?)
6. If the condition from point 4 is satisfied, we increase the value of the variable k (the counter for points contained in the circle of radius 1) by 1. If the condition is not met, we skip this step.
7. We increase the sampled point counter i by 1.
8. We check whether more points should be sampled (Is i≤number of points?). If yes, we return to step 3 of the algorithm.
9. We calculate and store the approximate value of π in the variable p (using the formula p=4⋅k/ik​).
10. We display the result.
11. STOP - The end of the algorithm.