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3. Pi In this problem, you are asked to write a C++ program which displays the value of Pi (1) using three different ways, as described in the three parts below, respectively. (a) Define a constant variable Pi and set it equal to 3.1416, which is a rounded value of n. You should use the proper data type and the variable should be a constant (i.e. its value cannot be changed in the program). (b) Approximate the value of t using the Gregory-Leibniz series shown below (instead of infinity as the upper limit, use a sufficiently large limit, e.g. 200). You can use the pow function from the library. 00 (-1)k 1 1 IT = 4 2k + 1 k=0 = 4 +--- +.. 7 (c) See problem 2 and its solution to be able to understand and solve this part Approximate the value of t using the Monte Carlo method with M (choose a sufficiently large M, e.g. M=1000000) random points. The idea is to generate M random points inside a square with side = 2 centered at the origin of the coordinate system. Then you need to count the number of points that fall within the unit circle (i.e. radius 1) centered at the origin (and so the circle is fully inside the square). Finally, you can approximate n by considering the following relation: Area of Square Area of Circle side? 22 4 TT x radius² Tn x 12 (d) Print the three values of pi obtained in parts a, b, and c above. You should get close results if M and the summation limit of part b are sufficiently large. Submit your solution in Pi.cpp.

3. Pi In this problem, you are asked to write a C++ program which displays the value of Pi (1) using three different ways, as described in the three parts below, respectively. (a) Define a constant variable Pi and set it equal to 3.1416, which is a rounded value of n. You should use the proper data type and the variable should be a constant (i.e. its value cannot be changed in the program). (b) Approximate the value of t using the Gregory-Leibniz series shown below (instead of infinity as the upper limit, use a sufficiently large limit, e.g. 200). You can use the pow function from the library. 00 (-1)k 1 1 IT = 4 2k + 1 k=0 = 4 +--- +.. 7 (c) See problem 2 and its solution to be able to understand and solve this part Approximate the value of t using the Monte Carlo method with M (choose a sufficiently large M, e.g. M=1000000) random points. The idea is to generate M random points inside a square with side = 2 centered at the origin of the coordinate system. Then you need to count the number of points that fall within the unit circle (i.e. radius 1) centered at the origin (and so the circle is fully inside the square). Finally, you can approximate n by considering the following relation: Area of Square Area of Circle side? 22 4 TT x radius² Tn x 12 (d) Print the three values of pi obtained in parts a, b, and c above. You should get close results if M and the summation limit of part b are sufficiently large. Submit your solution in Pi.cpp.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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3. Pi In this problem, you are asked to write a C++ program which displays the value of Pi (n) using three different ways, as described in the three parts below, respectively. (a) Define a constant variable Pi and set it equal to 3.1416, which is a rounded value of t. You should use the proper data type and the variable should be a constant (i.e. its value cannot be changed in the program). (b) Approximate the value of a using the Gregory-Leibniz series shown below (instead of infinity as the upper limit, use a sufficiently large limit, e.g. 200). You can use the pow function from the <math.h> library. (-1)* 1 1 TT = 4 = 4 + -- +.. 7. | 2k + 1 k=0 (c) See problem 2 and its solution to be able to understand and solve this part Approximate the value of t using the Monte Carlo method with M (choose a sufficiently large M, e.g. M=1000000) random points. The idea is to generate M random points inside a square with side = 2 centered at the origin of the coordinate system. Then you need to count the number of points that fall within the unit circle (i.e. radius 1) centered at the origin (and so the circle is fully inside the square). Finally, you can approximate n by considering the following relation: Area of Square side? 22 4 Area of Circle n x radius² Tn × 12 (d) Print the three values of pi obtained in parts a, b, and c above. You should get close results if M and the summation limit of part b are sufficiently large. Submit your solution in Pi.cpp.
Transcribed Image Text:3. Pi In this problem, you are asked to write a C++ program which displays the value of Pi (n) using three different ways, as described in the three parts below, respectively. (a) Define a constant variable Pi and set it equal to 3.1416, which is a rounded value of t. You should use the proper data type and the variable should be a constant (i.e. its value cannot be changed in the program). (b) Approximate the value of a using the Gregory-Leibniz series shown below (instead of infinity as the upper limit, use a sufficiently large limit, e.g. 200). You can use the pow function from the <math.h> library. (-1)* 1 1 TT = 4 = 4 + -- +.. 7. | 2k + 1 k=0 (c) See problem 2 and its solution to be able to understand and solve this part Approximate the value of t using the Monte Carlo method with M (choose a sufficiently large M, e.g. M=1000000) random points. The idea is to generate M random points inside a square with side = 2 centered at the origin of the coordinate system. Then you need to count the number of points that fall within the unit circle (i.e. radius 1) centered at the origin (and so the circle is fully inside the square). Finally, you can approximate n by considering the following relation: Area of Square side? 22 4 Area of Circle n x radius² Tn × 12 (d) Print the three values of pi obtained in parts a, b, and c above. You should get close results if M and the summation limit of part b are sufficiently large. Submit your solution in Pi.cpp.
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