RAMANUJAN METHOD

This method of computing is given by great mathematician Ramanujan. Ramanujan gave his own formula to calculate the value of using circle. The method is given below : Let PQR be a circle with center O of which a diameter is PR. Bisect PO at H and let T is the point of trisection OR nearer R. Draw TQ perpendicular to PR and place the chord RS = TQ. Join PS, and draw OM and TN parallel to RS. Place a chord PK = PM, and draw the tangent Pl = MN. Join RL, RK and KL. Cut off RC = RH. Draw CD parallel to KL meeting RD at D. Then the square on RD will be equal to circle PQR approximately.
     For         RS² = 5/36d²
     where d is diameter of circle.
     Therefore,         PS² = 31/36d
     But PL and PK are equal to MN and PM respectively.
     Therefore,          PK² = 31/144 d²,      and      PL² = 31/324 d².
     Hence, RK² = PR² - PK² = 113/144 d²,
     and RL² = PR² + PL² = 355/324.

But           RK/RL = RC/RD=3/2 sqrt(113/355) and         RC=3/4d.

HOW TO USE THIS APPLET:

Use of this Applet is very simple. You have to only select the diameter of the circle through combo box and in this Applet all the lines will be drawn automatically and the value of will be calculated. Actually, all the things in this method are based on the co-ordinate geometry. We have to calculate the co-ordinate when drawing the line.

Note :- If the area of the circle be 1450,000 square miles , then RD is greater than true length by an inch.