Kochanski's approximation is the following approximation for pi:
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
In the above figure, take 
, 
, and 
, so 
. Construct the circle centered
at 
with radius 1 and the circle
centered at 
with radius 1. These intersect
at 
and its reflection across 
. Now construct the circle centered
at 
with radius 1. The circles
centered at 
and 
intersect at 
and 
. The line 
intersects the perpendicular
to 
through 
at 
.
Extend 
beyond 
to 
with 
.
The line segment 
then has length
 |
(4)
|
This construction was given by the Polish Jesuit priest Kochansky (Steinhaus 1999).
