A circle of unit radius is completely covered by three identical squares. What is the smallest size of the squares?

Let two of the squares share an edge and the third centered above them, sharing half an ege with each.

  +---+

 a| d |b
+-+-+-+-+
|   o   |
+---+---+
    c

The circle is centered on the edge shared by the first two squares (o).  3 points on its perimeter are the bottom edge (c)and the two bottom corners of the top square (a and b).  d is the top edge of the bottom squares.

Call the square size x.  We have right triangle ado with
ad=x/2
do=1-x
ao=1

Pythagorean thm. gives (x-1)^2 + (x/2)^2 = 1
Solving gives x=0 or x=1.6

Posted by Jer on 2005-10-21 12:59:52