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## You're reading fromThe Modern C# Challenge

Product type Book
Published in Oct 2018
Publisher Packt
ISBN-13 9781789535426
Pages 362 pages
Edition 1st Edition
Languages
Concepts
Author (1):
Rod Stephens

Title Page
Dedication
Packt Upsell
Contributors
Preface
1. Mathematics 2. Geometry 3. Dates and Times 4. Randomization 5. Strings 6. Files and Directories 7. Advanced C# and .NET Features 8. Simulations 9. Cryptography 1. Other Books You May Enjoy Index

## Problems

Use the following problems to test your geometric programming skills. Give each problem a try before you turn to the solutions and download the example programs. If you have trouble with the graphical part, try to implement the non-graphical pieces. Then, you can download the example solutions and replace the key parts of the program with your code.

### 20. Monte Carlo π

A Monte Carlo algorithm uses randomness to approximate the solution to a problem. Often, using more random samples gives you a more accurate approximated solution or gives a greater probability that the solution is correct.

For this problem, use a Monte Carlo algorithm to approximate π. To do that, generate random points in the square (0 ≤ X, Y ≤ 1) and then see how many fall within a circle centered in that square.

### 21. Newton's π

Various mathematicians have developed many different ways to approximate π over the years. Sir Isaac Newton devised the following formula to calculate π:

Use Newton's method to approximate π. Let...

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