Kochanski's Approximation

The approximation for pi given by

			(1)
			(2)
			(3)

In the above figure, let , and construct the circle centered at  of radius 1. This intersects  at point . Now construct the circle about  with radius 1. The circles  and  intersect in , and the line  intersects the perpendicular to  through  in the point . Now construct the point  to be a distance 3 along . The line segment  is then of length

(4)

This construction was given by the Polish Jesuit priest Kochansky (Steinhaus 1999).

REFERENCES:

Bold, B. Famous Problems of Geometry and How to Solve Them. New York: Dover, p. 44, 1982.

Kochansky, A. A. "Observationes Cyclometricae ad facilitandam Praxin accomodatae." Acta Eruditorum 4, 394-398, 1685.

Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, p. 143, 1999.