For the following use a compass and straightedge procedure.

Given a unit square ABCD construct 4 circles centered at each corner and having diagonal radius. Form the smallest of the squares defined by the points where these circles intersect.

Use this process on the new square to create a third square.

1. Find and provide the area [in surd format] of each square so formed.

2. Following this process find a general expression for the area of the n^th square.

(In reply to re: solution by brianjn)

Ooops. When writing the general formula, I switched the base with the exponent in the denominator.  I've corrected the original comment and noted the change.

Posted by Charlie on 2011-01-31 10:20:10