*Problem #49*

A spiral path is constructed in the unit square whose vertices have
coordinates (0,0), (1,0), (1,1), and (0,1) as follows. Let A_{1}
= (0,1), A_{2} = (1,1), A_{3} = (1,0), and A_{4} =
(0,0). Let A_{5} be the midpoint of A_{1}A_{2},
A_{6} be the midpoint of A_{2}A_{3}, A_{7}
be the midpoint of A_{3}A_{4}, etc. This forms a spiral
polygonal path A_{1}A_{2}A_{3}A_{4}...
converging to a unique point in the plane. Find the coordinates of this
point.
**Source: Len Bos and Bill Sands**