Qno1 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^2
(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
Now the big question is how do you calculate the area of the gray 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 gray shaded quadrant or
outside. Hint: sqrt(x^2 + y^2 ).
- 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 gray shaded area.
- Apply this to your equation to find the mathematical constant PI.
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