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Calculate the mathematical constant of PI
THE WEEKEND TEASER:
Write a C++ program to calculate the mathematical constant of PI:
(a) Imagine a circle, whose area is given by: Area=PI*R^2
(b) Now imagine that you divide the circle exactly into 4 quadrants.
(c) The area of one quadrant is hence: Area=0.25*PI*R (d) Now let us set the radius to be R=1;
(e) The equation hence becomes: Area=0.25*PI
(f) So we can simply say: PI = Area*4
y-axis
x=0 y=1
x=0 y=0
Note that this square is 1.0 x 1.0 in size.
x-axis
x=1 y=0
Now the big question is how do you calculate the area of the grey shaded quadrant of the circle above? Use a random number generator and guess effectively the correct answer. (Hint: use rand() from <cstdlib> and make sure that you divide through by RAND_MAX.)
The technique you should use is to:
- guess a random number between 0.00 and 1.00 and assign this to x.
- guess a random number between 0.00 and 1.00 and assign this to y.
- find out if this (x,y) coordinate lies inside the grey shaded quadrant or
outside. Hint: sqrt(x +y ).
- Repeat these steps N times, where N is sufficiently big and then find the ratio of points inside the circle divided by the total number N, to determine the area of the grey shaded area.
- Apply this to your equation to find the mathematical constant PI.
Write a C++ program to calculate the mathematical constant of PI:
(a) Imagine a circle, whose area is given by: Area=PI*R^2
(b) Now imagine that you divide the circle exactly into 4 quadrants.
(c) The area of one quadrant is hence: Area=0.25*PI*R (d) Now let us set the radius to be R=1;
(e) The equation hence becomes: Area=0.25*PI
(f) So we can simply say: PI = Area*4
y-axis
x=0 y=1
x=0 y=0
Note that this square is 1.0 x 1.0 in size.
x-axis
x=1 y=0
Now the big question is how do you calculate the area of the grey shaded quadrant of the circle above? Use a random number generator and guess effectively the correct answer. (Hint: use rand() from <cstdlib> and make sure that you divide through by RAND_MAX.)
The technique you should use is to:
- guess a random number between 0.00 and 1.00 and assign this to x.
- guess a random number between 0.00 and 1.00 and assign this to y.
- find out if this (x,y) coordinate lies inside the grey shaded quadrant or
outside. Hint: sqrt(x +y ).
- Repeat these steps N times, where N is sufficiently big and then find the ratio of points inside the circle divided by the total number N, to determine the area of the grey shaded area.
- Apply this to your equation to find the mathematical constant PI.
Please note, that this is not a homework site. We won't do your homework for you. However we are always willing to help solve problems you encountered, correct mistakes you made in your code and answer your questions.
We didn't see your attemts to solve this problem youself and so we cannot correct mistakes you didn't made and answer questions you didn't ask. To get help you should do something yourself and get real problems with something. If your problem is "I don't understand a thing", then you should go back to basics and study again. As it is impossible to find deriviative of function without knowledge in ariphmetics, you cannot do more complex tasks in programming without clear understanding of basics
We didn't see your attemts to solve this problem youself and so we cannot correct mistakes you didn't made and answer questions you didn't ask. To get help you should do something yourself and get real problems with something. If your problem is "I don't understand a thing", then you should go back to basics and study again. As it is impossible to find deriviative of function without knowledge in ariphmetics, you cannot do more complex tasks in programming without clear understanding of basics
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