-1

Using the √2 = 1.41421356237... as a target, the connection I see is that you can approximate √2 first by taking the distance between 1 and 2 to get 1.5 or 1 1/2, then, since that is greater than √2, divide the distance between 1 and 1.5 in two to get 1.25 or 1 1/4, and then, since that is less t...