I was going through physics competition problems on http://fykos.org/ when I stumbled across this one:
... The Square The Joker
The electric circuit in the image is made from the infinite number of wire-frame-squares. The next square is exactly sqrt(2) smaller then the previous. The resistance of used wire is R per one side of the largest square. What is electrical resistance between most left and most right point?
I have tried to solve it but just can't seem to get it. They've attached their solution to the same page which can be found here although it is in Czech and I can't understand it nor the mathematics behind what they're doing.