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Estimation of PI

Points inside the circle

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Points outside the circle

0

Total

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Value of Pi(π)

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Percentage error

0

#### OBJECTIVE

The aim is to estimate the value of Pi by using Monte Carlo estimation method.

#### DESCRIPTION

The Monte Carlo method is a powerful computational technique that uses random sampling to obtain numerical results. One of its most famous applications is estimating the value of Pi. The method involves generating a large number of random points within a square and then determining how many of those points fall within a quarter circle inscribed. The Monte Carlo method is a powerful computational technique that uses random sampling to obtain numerical results. One of its most famous applications is estimating the value of Pi. The method involves generating a large number of random points within a square and then determining how many of those points fall within a quarter circle inscribed in that square. The ratio of the number of points within the quarter circle to the total number of points generated provides an estimate for Pi.

#### SIGNIFICANCE

The significance of the Monte Carlo method in estimating the value of Pi lies in its ability to produce highly accurate results with relatively few calculations. By generating a large number of random points and repeating the process multiple times, the Monte Carlo method can converge to the true value of Pi with a high degree of accuracy. Additionally, the method is easily parallelizable, making it well-suited for use in high-performance computing environments.

#### QUIZ

1. Monte Carlo method is a technique used to solve mathematical problems using

2. Which of the following problems can be solved using the Monte Carlo method?

3. The Monte Carlo method is based on:

4. The value of Pi can be estimated using the Monte Carlo method by:

5. To increase the accuracy of the estimated value of Pi using the Monte Carlo method, we should:

#### Contributors

Dr. Anuj Krishna and entire Team JIGYASA, CSIR-NPL