Kochanski's Approximation
The approximation for pi given by
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.
