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 solution by Charlie)

Ah, we are now in full agreement.

Interestingly though my general formula looks different to yours but in reality is essentially the same.

The area of my first constructed square was:
  (√7 - 1)² / 2
=(1 - 2√7 + 7) / 2
=(8 - 2√7) / 2
=(4 - √7)

Note Charlie's given value for that square is in the first line.

Edited on January 31, 2011, 7:30 pm

Posted by brianjn on 2011-01-31 19:20:14