PIEXPT.F95

	PROGRAM PIEXPT
!
!  Purpose: To obtain an approximate value of pi.
!
	IMPLICIT NONE
	INTEGER::I	
	INTEGER::N,NCIRCLE	
	REAL:: X,Y	
	REAL:: PIAPPR	
!
	WRITE(*,*)'How many points ?'
	READ(*,*)N
!
!  Initialize NCIRCLE and draw N random points.
	NCIRCLE=0
	DO I=1,N
 	  CALL RANDOM_NUMBER(X)
 	  CALL RANDOM_NUMBER(Y)
!  Redefine X and Y so as to have values distributed between -1 and +1,
!  rather than between 0 and 1 (as returned by RANDOM_NUMBER).
	  X = 2.*(X-0.5)
	  Y = 2.*(Y-0.5)
!
!  Method: the area of a circle circumscribed in the square is exactly pi,
!  since the radius is 1. The area of the square is exactly 4. Since the random
!  points are uniformly distributed, the ratio of the area of the circle
!  to the area of the square is approximately equal to the ratio of the number
!  of random points falling inside the circle to the quarter of the total
!  number of random points.
!
	  IF(X**2+Y**2 <= 1)NCIRCLE=NCIRCLE+1
	END DO
!
!  Approximate value of pi
	PIAPPR=4.*REAL(NCIRCLE)/REAL(N)
	WRITE(*,*)'Approximate value: ',PIAPPR
	WRITE(*,*)'Exact value:       ',4.*ATAN(1.)
	
	STOP
	END PROGRAM PIEXPT